Suppose we want to choose 6 objects, without replacement, from 14 distint objects. How many ways can this be done, if the order of the choices is not relevant?

Answer 1

This is the combination of 14 "things" taken 6 at a time (order does not matter).

₁₄C₆ = 14! / [(14-6)! 6!] = 14(13)(12)(11)(10)(9)/ (6)(5)(4)(3)(2)

Notice there are 6 factors in the numerator. Instead of memorizing the formula, I like to think:

start writing14! but stop after 6 factors, then divide by 6!.

Check out how to do this on Desmos:

desmos.com/calculator/3pmafmwwac