Cricket Team
Probability
Level
2
A cricket team of 11 players is to be selected from two groups of 6 and 8 players. In how many ways can the selection be made so that at least 4 players are taken from the group of 6?
The answer is 344.
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1 solution
Number of ways to choose 4 people from team of 6:
( 4 6 ) ( 7 8 ) = 1 5 × 8 = 1 2 0
Number of ways to choose 5 people from team of 6:
( 5 6 ) ( 6 8 ) = 6 × 2 8 = 1 6 8
Number of ways to choose 6 people from team of 6:
( 6 6 ) ( 5 8 ) = 1 × 5 6 = 5 6
Total number of ways = 1 2 0 + 1 6 8 + 5 6 = 3 4 4 ways