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Suppose i have the given data set of length 11 of scores p=[2, 5, 1 ,2 ,4 ,1 ,6, 5, 2, 2, 1]

I want to select 6 ,5 , 5 , 4 , 2 , 2 scores from the data set.

How many ways are there?

For the above example answer is:: 6 ways

{p1, p2, p4, p5, p7, p8 }

{p10, p2, p4, p5, p7, p8 }

{p1, p2, p10, p5, p7, p8 }

{p9, p2, p4, p5, p7, p8 }

{p1, p2, p9, p5, p7, p8 }

{p10, p2, p9, p5, p7, p8 }

So what is the formula??

  • 0
    [Crossposted on cs.SE](http://cs.stackexchange.com/q/1444/98).2012-04-23

1 Answers 1

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$p$ has one 6, two 5s, one 4, zero 3s, four 2s and three 1s.

You want to select one 6, two 5s, one 4, zero 3s, two 2s and zero 1s.

So the formula is ${1 \choose 1} \times {2 \choose 2} \times {1 \choose 1} \times {0 \choose 0} \times {4 \choose 2} \times {3 \choose 0}$ $= 1 \times 1 \times 1 \times 1 \times 6 \times 1 =6.$