Example 1 · level 1
In how many ways can 4 books be chosen from 10 different books? That is, find 10C4.
Show solution
- 10 × 9 × 8 × 7 = 5,040.
- ÷ 4! = 24 → 210.
Answer: 210
CLASS 11 MATHS · PERMUTATIONS AND COMBINATIONS
Permutations and combinations
Order matters → permutations, ⁿPᵣ = n!/(n − r)!. Order does not matter → combinations, ⁿCᵣ = n!/(r!(n − r)!). Repeated letters: divide by the factorial of each repeat count.
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Worked examples
Example 2 · level 2
How many different arrangements can be made using all the letters of the word HAMPI?
Show solution
- 5! = 120.
- Answer: 120.
Answer: 120
Example 3 · level 3
A school in Ranchi must pick a quiz team of 2 boys and 3 girls from 7 boys and 8 girls. In how many ways can the team be chosen?
Show solution
- 7C2 = 21.
- 8C3 = 56.
- Ways = 21 × 56 = 1,176.
Answer: 1,176