CA Foundation · Quantitative Aptitude · Permutations and Combinations
A club in Kochi has 7 members who play cricket and 6 members who play football, and no member plays both. A team of 5 is to be chosen consisting of exactly 3 cricket players and 2 football players. In how many ways can this be done?
The team can be chosen in 525 ways. Select 3 cricketers from 7 in 35 ways and 2 footballers from 6 in 15 ways, then multiply the independent choices: 35 x 15 = 525.
- A525Correct
- B1287
- C420
- D350
Explanation
Choose 3 of 7 cricket players: 7C3 = 35. Choose 2 of 6 football players: 6C2 = 15. Multiply: 35 x 15 = 525. The option 1287 is 13C5, which ignores the composition condition. The option 350 comes from 35 x 10 using 5C2 wrongly.
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