Answer to Question #181340 in Discrete Mathematics for ali

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.