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Thread: [SOLVED] Permutation and Combination Question 1

  1. #1
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    [SOLVED] Permutation and Combination Question 1

    How manu four-digit numbers greater than 5000 can be formed from the digits 0,1,2,3,4,5 if
    a) all digits may be repeated (I get 215, I just want to confirm if I am right)
    b) only the digit 4 may be repeated?
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  2. #2
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    Quote Originally Posted by azuki View Post
    how manu four-digit numbers greater than 5000 can be formed from the digits 0,1,2,3,4,5 if
    a) all digits may be repeated (i get 215,) correct
    b) only the digit 4 may be repeated?
    correct
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  3. #3
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    Hello, azuki!

    How many four-digit numbers greater than 5000
    can be formed from the digits 0,1,2,3,4,5 if

    b) only the digit 4 may be repeated?
    The first digit must be 5: .$\displaystyle 5\:\_\:\_\:\_$


    There are 4 cases to consider . . .

    (1) No 4's
    Then we have a choice of {0, 1, 2, 3}.
    . . The second digit has 4 choices.
    . . The third digit has 3 choices.
    . . The fourth digit has 2 choices.
    There are: .$\displaystyle 4\cdot3\cdot2 \:=\:{\color{blue}24}$ numbers with no 4's.

    (2) One 4
    There are 3 possible positions for the 4.
    . . The other two digits have: $\displaystyle 4\cdot3 \:=\:12$ choices.
    There are: .$\displaystyle 3\cdot12 \:=\:{\color{blue}36}$ numbers with one 4.

    (3) Two 4's
    There are 3 possible positions for the two 4's.
    . . There are $\displaystyle 4$ choices for the fourth digit.
    There are: .$\displaystyle 3\cdot4\:=\:{\color{blue}12}$ numbers with two 4's.

    (4) Three 4's.
    There is only $\displaystyle {\color{blue}1}$ number with three 4's: .$\displaystyle 5444$


    Answer: .$\displaystyle 24+ 36 + 12 + 1 \:=\:73$ numbers.

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