What is the number of sets of five elements that can be formed from 11 elements set

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We'll recall the formula that gives the number of combinations of n elements taken k at a time:

(n,k) = n!/k!(n-k)! (1)

To determine the number of gropus of 5 that can be formed from 11 elements, we'll use (1):

(11,5) = 11!/5!(11-5)!

(11,5) = 11!/5!*6!

But 11! = 6!*7*8*9*10*11

5! = 1*2*3*4*5

We'll replace 11! and 5! and we'll get:

(11,5) = 6!*7*8*9*10*11/1*2*3*4*5*6!

We'll simplify and we'll get:

(11,5) = 7*2*3*11

(11,5) = 462

The number of combinations of 5 elements, that can be formed from 11  elements, is (11,5) = 462.

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