how to divide 22 players into a team of 11 in every combination

Question

there are 22 players and I ned to know how many combinations would be there if we make a team of 11

like how many ways are there to make a team of 11 out of 22

Answer 1

This is a direct application of a combinatorial selection problem. If you have n objects of which you wish to select r, then you can do so in ⁿC_r ways. The mathematical formula to calculate ⁿC_r is -

ⁿC_r = n! / ( (n-r)! r! ) where the "!" sign denotes the factorial.

Note that the denominator is the product of (n-r)! and r!

For this specific problem, n = 22 and r = 11

Answer = ²²C₁₁

= 22! / (11! x 11!) ...answer