First slide

Combinations

Question

The number of ways in which two teams A and B of 11 players each can be made up from 22 players so that two particular players are on the opposite sides is

Moderate

A

369512
B

184755
C

184756
D

369514

Solution

We can choose 10 players from (22 – 2) players in ${}^{20}C_{10}$ ways and one player from 2 players in ${}^{2}C_{1}$ ways.
$∴$ required number of ways
$= \frac{20!}{10! 10!} \times 2 = 369512$

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