Example 1 · level 1
In how many ways can 2 different prizes (first, second) be given to 7 students, at most one prize each?
Show solution
- 7P2 = 7 × 6 = 42.
Answer: 42
CA FOUNDATION: QUANTITATIVE APTITUDE · PERMUTATIONS AND COMBINATIONS
Permutations and combinations
Order matters → nPr = n!/(n − r)!. Order does not matter → nCr = n!/[r!(n − r)!].
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Worked examples
Example 2 · level 2
In how many ways can 2 different prizes (first, second) be given to 5 students, at most one prize each?
Show solution
- 5P2 = 5 × 4 = 20.
Answer: 20
Example 3 · level 3
An audit team of 3 men and 1 women is to be chosen from 6 men and 3 women articled assistants. In how many ways can this be done?
Show solution
- Men: 6C3 = 20.
- Women: 3C1 = 3.
- Total = 20 × 3 = 60.
Answer: 60