# How many possible ways are there

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
–  Raphael Apr 23 '12 at 7:01

$p$ has one 6, two 5s, one 4, zero 3s, four 2s and three 1s.
So the formula is $${1 \choose 1} \times {2 \choose 2} \times {1 \choose 1} \times {0 \choose 0} \times {4 \choose 2} \times {3 \choose 0}$$ $$= 1 \times 1 \times 1 \times 1 \times 6 \times 1 =6.$$