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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??

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Apparently the formula is "6". What is the general question? –  JeffE Apr 22 '12 at 16:59
    
I want to ask how can we get answer using combination formula..Suppose the data set of 11 items D are there i want to choose n items {k1,k2,k3..kn} from the data set how many ways are there? –  Maths123 Apr 22 '12 at 17:05
1  
Why is your accept rate 0%? You can tick the check mark next to an answer if it is satisfactory . . . –  Joe Apr 22 '12 at 17:44
    
Crossposted on cs.SE. –  Raphael Apr 23 '12 at 7:01

1 Answer 1

up vote 3 down vote accepted

$p$ 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 $${1 \choose 1} \times {2 \choose 2} \times {1 \choose 1} \times {0 \choose 0} \times {4 \choose 2} \times {3 \choose 0}$$ $$= 1 \times 1 \times 1 \times 1 \times 6 \times 1 =6.$$

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