A men's basketball league assigns every player

BTGmoderatorDC wrote:A men's basketball league assigns every player a two-digit number for the back of his jersey. If the league uses only the digits 1-5, what is the maximum number of players that can join the league such that no player has a number with a repeated digit (e.g. 22), and no two players have the same number?

A. 20
B. 21
C. 22
D. 24
E. 25

Can some experts show me the best solution in this?

OA A

We need to determine how many two-digit numbers can be created from 5 digits (1 to 5, inclusive), and no digits can be repeated. Since order matters, we have a permutation. Thus, the number of ways to create two-digit numbers is 5P2 = 5!/(5 - 2)! = 5 x 4 = 20.

Alternate Solution:

If repeated digits were allowed, there would be 25 possibilities since for each digit we would have 5 choices. Among these 25 possibilities, 5 of them are repeated digit numbers (which are 11, 22, 33, 44, and 55). Thus, without the repeated digits, there are 25 - 5 = 20 numbers possible.

Answer: A