Question

An urn contains numbered balls. How many ways can we choose balls out of the urn (without repetition, the order does not count)6

63

Answer 1

Let's say we have 63 balls in the urn, and need to choose 6 balls. Six balls have 6! orders, thus the number of choices for choosing 6 balls out of 63 without any repetition such that the order does not count is $\dfrac{63!}{57!\times6!}$ = 407673126.