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Math Help - Counting problem

  1. #1
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    Counting problem

    Let S = {1,2,3,4,5}
    (a) List all the 3-permutations of S
    (a) List all the 3-combinations of S

    Can any one help me with this ??
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  2. #2
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    Quote Originally Posted by bhuvan View Post
    Let S = {1,2,3,4,5}
    (a) List all the 3-permutations of S
    (a) List all the 3-combinations of S

    Can any one help me with this ??
    a) 5C3 = 5!/(3!*(5-3)!) = 10 (order doesn't matter)
    b) 5P3 = 5!/(5-3)! = 60 (order matters)

    a)
    {1,2,3}
    {1,2,4}
    {1,2,5}
    {1,3,4}
    {1,3,5}
    {1,4,5}
    {2,3,4}
    {2,3,5}
    {2,4,5}
    {3,4,5}
    Total = 10



    b)
    {1,2,3}
    124
    125
    132
    134
    135
    142
    143
    145
    152
    153
    154
    .
    .
    .
    should add up to 60
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  3. #3
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    Hello, bhuvan!

    Let S \:=\: \{1,2,3,4,5\}

    (a) List all the 3-permutations of S
    There are _5P_3 \:=\:\tfrac{5!}{2!} \:=\:60 of them.

    I'll start the list . . .

    . . \begin{array}{cccccccccccc}<br />
123 & 124 & 125 & 132 & 134 & 135 & 142 & 143 & 145 & 152 & 153 & 154 \\ \\[-4mm]<br />
213 & 214 & 215 & 231 & 234 & 235 & 241 & 243 & 245 & 251 & 253 & 254 \\ \\[-4mm]<br />
312 & 314 & 315 & 321 & 324 & 325 & 341 & 342 & 345 & 351 & 352 & 354 \\<br />
& & & & \hdots & \text{etc.} & \hdots\end{array}



    (b) List all the 3-combinations of S
    There are _5C_3 \:=\:\tfrac{5!}{3!2!}  \:=\:10 of them . . .

    . . \begin{array}{ccccc}(1,2,3)&(1,2,4)&(1,2,5)&(1,3,4  )&(1,3,5) \end{array} . \begin{array}{ccccc}(1,4,5)&(2,3,4)&(2,3,5)&(2,4,5  )&(3,4,5) \end{array}



    Edit: . Ha! TitaniumX beat me to it . . .
    .
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  4. #4
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    thank you very much ...

    How many solutions are there to the equation

    x1+x2+x3+x4=17

    where x1,x2,x3 and x4 are nonnegative integers ??

    appreciate your reply.
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  5. #5
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    Quote Originally Posted by bhuvan View Post
    How many solutions are there to the equation
    x1+x2+x3+x4=17. where x1,x2,x3 and x4 are nonnegative integers ??
    The number of ways to put N identical ones into k different variables (non-negative integers) is {{N+k-1} \choose {N}}.
    Here N=17 and k=?
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  6. #6
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    can you please give me one example of that ??
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