IPL Fever #3
An IPL match is going to take place between two teams Mumbai Indians and Chennai Super Kings.
It has been found out that the captain of Chennai Super Kings , Mahendra Singh Dhoni and the vice-captain, Brendon McCullum are injured and they wouldn't be able to play the match. The team management is very upset and decide to elect a new squad of players. The total team strength consists of players out of which two are injured.
In how many ways can the team management select players for the match from the remaining players and a new captain and new vice-captain?
The answer is 150150.
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1 solution
Total Team Strength = 1 7
Injured players = 2
Remaining Squad = 1 5
Number of ways of electing 1 1 out of 1 5 = 4 ! × 1 1 ! 1 5 ! = 1 3 6 5 .
In each chosen team there are 1 1 ways of electing a captain and there are 1 0 ways of electing a vice-captain.
Total number of ways of electing a squad of 1 1 = 1 3 6 5 × 1 1 × 1 0
= 1 5 0 1 5 0