Calculate the number of combinations of 11 items taken 4 at a time.

Question

Calculate the number of combinations of 11 items taken 4 at a time.

Answer 1

Assuming that all the objects are different:

There are 11 possibilities for the 1st object. Each time an object is taken, there is one fewer to chose from.

Complete this list, and then multiply the values together:

1st object: 11 choices

2nd object: 10 choices

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Answer 2

_nC_r = n! = 11! = (11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1) = (11)(10)(9)(8) = (11)(5)(3)(2) = 330

r!(n-r)! 4!(11-4)! (4)(3)((2)(1)(7)(6)(5)(4)(3)(2)(1) (4)(3)(2)(1)

I simplified by canceling numbers in the numerator and denominator.