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Math Help - ~~help ASAP assignment 2!!!

  1. #1
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    ~~help ASAP assignment 2!!!

    can any one do assignment 2 as soon as possible?

    when u have answer plz explain how did u get it.....and show every steps plz......thnx very much



    thank you u all.....thnx so much
    Last edited by kansairacing; June 19th 2006 at 04:52 PM.
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  2. #2
    Super Member malaygoel's Avatar
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    Question no.2

    Quote Originally Posted by kansairacing
    can any one do assignment 2 as soon as possible?

    when u have answer plz explain how did u get it.....and show every steps plz......thnx very much

    we have to form six digit numbers taking care of 1,9,0.
    for the first digit we can use 7 numbers(2,3,4,5,6,7,8)
    for the second digit we can use 8 numbers(0,2,3,4,5,6,7,8)
    for the third digit we can use 8 numbers(0,2,3,4,5,6,7,8)
    for the fourth digit we can use 8 numbers(0,2,3,4,5,6,7,8)
    for the fifth digit we can use 8 numbers(0,2,3,4,5,6,7,8)
    for the sixth digit we can use 8 numbers(0,2,3,4,5,6,7,8)
    hence total possible numbers = 7*8*8*8*8*8
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  3. #3
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    Quote Originally Posted by kansairacing
    plz hlep me........i need it ASAP...............
    What do you not understand about malaygoel's answer?

    RonL
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  4. #4
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    Hello, kansairacing!

    Is it true that you can't do any of these? . . . sorry to hear it!

    Here are a few of them . . .

    8. John Finds 10 shirts in his size at a clearance sale.
    How many different purchases could he make?
    For each of the ten shirts, he has a two-way decision: buy or not-buy.

    Therefore, there are: 2^{10} = 1024 decisions/purchases he can make.

    [Note: this includes the decision to buy no shirts.]

    10. A school dance has 10 volunteers. .Each dance requires 2 volunteers at the door,
    3 volunteers on the floor, and 5 floaters. .If two of the volunteers, John and Tom,
    can not work together, in how many ways can the volunteers be assigned?
    There are: \binom{10}{2,3,5}\:=\:\frac{10!}{2!3!5!}\:=\;2520 ways to make the assignments.

    We will count the number of ways that John and Tom are together.
    Duct-tape them together; then we have nine "people" to arrange.
    . . \{JT,\;A,\;B,\;C,\;D,\,E,\;F,\;G,\:H\}

    If JT are at the door, the other 8 people can be assigned in
    . . \binom{8}{3,5} \:=\:\frac{8!}{3!5!}\:=\:56 ways.

    If JT are on the floor, the other 8 people can be assigned in
    . . \binom{8}{2,1,5}\:=\:\frac{8!}{2!1!5!}\:=\:126 ways.

    If JT are floaters, the other 8 people can be assigned in
    . . \binom{8}{2,3,3}\:=\:\frac{8!}{2!3!3!}\:=\:560 ways.

    Hence, there are: 56 + 126 + 560\,=\,742 ways that John and Tom are together.


    Therefore, there are: 2520 - 742 \,=\,1778 ways that they are not together.

    *
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  5. #5
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    Hello, kansairacing!

    Here's #3.
    [I assume you know that there is an "E" in MATHEMATICS . . .

    Find the number of ways arranging the letters of MATHMATICS if:
    (a) there are no restrictions
    (b) the first letter must be C
    (c) the EVEN-numbered position must remain unchanged.
    (d) the letters C and H must be separated
    There are 10 letters, including 2 A's, 2 M's, and 2 T's.

    (a) With no restrictions, there are: \frac{10!}{2!2!2!}\;=\;453,600 ways.


    (b) If the first letter must be C, the other nine letters can be arranged in:
    . . . \frac{9!}{2!2!2!}\:=\:45,360 ways.


    (c) If the even-numbered positions are unchanged, we have: \_\ A\_\ H\_\ A\_\ I\_\ S
    Then the remaining \{C,M,M,T,T\} can have \frac{5!}{2!2!}\:=\;30 arrangements.


    (d) We will count the way that C and H are together.

    Duct-tape them together.
    Then we have nine "letters" to arrange: \{\overline{CH}, A, A, I, M, M, S, T, T\}
    . . These can be arranged in \frac{9!}{2!2!2!}\:=\:45,360 ways.

    But C and H could have been taped like this: \{\overline{HC},A,A,I,M,M,S,T,T\}
    . . And these can be arranged in another 45,360 ways.

    Hence, there are: 2 \times 45,360\:=\:90,720 ways for C and H to be together.


    Therefore, there are: 453,600 - 90,720\:=\:362,800 for C and H to be separated.
    Last edited by CaptainBlack; July 16th 2006 at 07:25 AM.
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  6. #6
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    6. (8 marks) Develop a formula relating t_{n,r} of Pascal's triangle to the terms in row n-2.


    For the sake of convenience take:

    <br />
t_{n,r}=0,\ \mbox{for }r>n,\ \mbox{ or } r<1<br />

    Then the basic relation between the entries in one row and the preceeding
    row in Pascal's triangle is:

    <br />
t_{n,r}=t_{n-1,r-1}+t_{n-1,r}\ \ \ \dots (1)<br />
,

    so applying the rule to the first term of the right hand side of the above:

    <br />
t_{n-1,r-1}=t_{n-2,r-2}+t_{n-2,r-1}<br />
,

    and to the second term:

    <br />
t_{n-1,r}=t_{n-2,r-1}+t_{n-2,r}<br />
.

    Substituting these into (1) gives:

    <br />
t_{n,r}=t_{n-2,r-2}+2t_{n-2,r-1}+t_{n-2,r}<br />
.

    RonL
    Last edited by CaptainBlack; July 16th 2006 at 07:23 AM.
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  7. #7
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by malaygoel
    we have to form six digit numbers taking care of 1,9,0.
    for the first digit we can use 7 numbers(2,3,4,5,6,7,8)
    for the second digit we can use 8 numbers(0,2,3,4,5,6,7,8)
    for the third digit we can use 8 numbers(0,2,3,4,5,6,7,8)
    for the fourth digit we can use 8 numbers(0,2,3,4,5,6,7,8)
    for the fifth digit we can use 8 numbers(0,2,3,4,5,6,7,8)
    for the sixth digit we can use 8 numbers(0,2,3,4,5,6,7,8)
    hence total possible numbers = 7*8*8*8*8*8
    I disagree, in one of those 6 digits you have to use a zero.

    So you would find the number of combinations without zero, which is 7^6=117,649

    Then you would subtract that number from the total possible combinations, 7*8^5-7^6=111,727

    and that leaves you with the number of six-digit numbers that contain zero
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  8. #8
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    Hello again, kansairacing!

    Since there is disagreement about #2, here's my solution . . .

    2. How many 6-digit numbers are there that include the digit 0
    and exclude the digits 1 and 9?
    Find the number of six-digit numbers that exclude 1 and 9.
    For each of the six digits, there are 8 choices: . 8^6 numbers.

    Among these, how many exclude 0?
    For each of the six digits, there are 7 choices: . 7^6 numbers.


    The difference is number of 6-digit numbers that exclude 1 and 9 and include 0:

    . . . 8^6 - 7^6\:=\:262,144 - 117,649\:=\:144,495
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  9. #9
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    Quote Originally Posted by Soroban
    Hello again, kansairacing!

    Since there is disagreement about #2, here's my solution . . .


    Find the number of six-digit numbers that exclude 1 and 9.
    For each of the six digits, there are 8 choices: . 8^6 numbers.

    Among these, how many exclude 0?
    For each of the six digits, there are 7 choices: . 7^6 numbers.


    The difference is number of 6-digit numbers that exclude 1 and 9 and include 0:

    . . . 8^6 - 7^6\:=\:262,144 - 117,649\:=\:144,495
    The first digit can't have 0, which leaves only seven different numbers possible for the first digit, because no number greater than 1 starts with 0.
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  10. #10
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    how do u do nubmer 7, 9?

    i dont understand the question...
    Last edited by kansairacing; June 18th 2006 at 08:33 PM.
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  11. #11
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    Hello, Quick!

    The first digit can't have 0 . . .
    You're right . . . I forgot that convention . . . *blush*
    I'll try again.

    2. How many 6-digit numbers are there that include the digit 0
    and exclude the digits 1 and 9?
    Find the number of six-digit numbers that exclude 1 and 9.

    The first digit cannot be 0; there are 7 choices.
    Each of the remaining five digits has 8 choices.
    . . Hence, there are: 7\cdot8^5 numbers.

    Among these, how many exclude 0?
    . . For each of the six digits, there are 7 choices: . 7^6 numbers.


    The difference is number of 6-digit numbers that exclude 1 and 9 and include 0:

    . . . 7\cdot8^5 - 7^6\:=\:229,376 - 117,649\:=\:111,727
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  12. #12
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    Hello, kansairacing!

    It would be gratifying to get some feedback . . .
    . . Are we helping at all?
    . . Is there any learning taking place?
    . . Or are we just doing your homework for you?

    7) Suppose you are designing a remote control that uses short or long pulses
    of infrared light to send control signals to a device.
    (a) How many different codes can you defined using two or three pulses?
    (b) Explain how the Rule of Product and the Rule of Sum apply in your calculation.
    (a) The very least you could do is list the possibilities . . . right?

    With two pulses: LL,\;LS,\;SL,\;SS . . . 4 signals.
    With three pulses: LLL,\;LLS,\,LSL,\,LSS,\;SLL,\;SLS,\;SSL,\;SSS . . . 8 signals.
    . . Answer: 4 + 8 \,=\,12 signals.

    (b) Two pulses: for each of the two pulses, there are two choices, L or S.
    . . Hence, there are: 2^2 = 4 two-pulse signals.
    Three pulses: for each of the three pulses, there are two choices.
    . . Hence, there are: 2^3 = 8 three-pulse signals.
    These two steps use the Rule of Product.

    Therefore, for two or three pulses, there are: 4 + 8 \,=\,12 signals.
    This step uses the Rule of Sum.


    9) Suppose the Canadian Embassy in the Netherlands has 28 employees.
    Eight of the employees speak German and ten speak Dutch.
    If two empolyees speak both German and Dutch,
    how many of the employees speak neither German nor Dutch?
    Illustrate your answer with a Venn diagram.
    Code:
          * - - - - - - - - - - - - - - *
          |                             |
          |     * - - - - - *           |
          |     | G   6     |           |
          |     |     * - - + - - *     |
          |     |     |  2  |     |     |
          |     * - - + - - *     |     |
          |           |     8   D |     |
          |           * - - - - - *     |
          |   12                        |
          * - - - - - - - - - - - - - - *
    The large rectangle represents the 28 employees.

    We are told that 2 speak German and Dutch.
    The "2" goes in the region common to the German square and the Dutch square.

    Since 8 of them speak German, there are 6 who speak only German.
    Since 10 of them speak Dutch, there are 8 who speak only Dutch.

    We have accounted for: 6 + 2 + 8 \,= \,16 of the employees.

    Therefore, the other 28 - 16 \,=\,12 are those who speak neither German nor Dutch.
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  13. #13
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    Quote Originally Posted by Soroban
    Hello, kansairacing!

    It would be gratifying to get some feedback . . .
    . . Are we helping at all?
    . . Is there any learning taking place?
    There certainly is on the part of the helpers

    . . Or are we just doing your homework for you?
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  14. #14
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    THank you all...............i love u all very much........thnx
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