Question

In how many ways can the 19 members of a chess club fill the offices of​ King, Knight,​ Bishop, and​ Rook?

Answer 1

Solution:

This problem is a permutation because the order matters here. This means that choosing A as King, B as Knight, C as Bishop and D as Rook results in a different arrangement from B as King, A as Knight, D as Bishop and C as Rook. We would count them both because in the first case A is King, but in the second case A is Knight.

Therefore, the possible number of ways are given below:

$19P4=\frac{19!}{(19-4)!} =\frac{19 \times 18 \times 17 \times 16 \times 15!}{15!} =19 \times 18 \times 17 \times 16 =93024$

Hence there will be 93024 ways 19 members of a chess club fill the offices of King, Knight, Bishop, and Rook.