Selections and committees: Class 11 practice
Use combinations when order doesn't matter: ⁿCᵣ = n!/(r!(n − r)!). Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Factorials
- ⁿCᵣ
The idea behind selections and committees
Use combinations when order doesn't matter: ⁿCᵣ = n!/(r!(n − r)!). For mixed groups, multiply the choices for each part. 'At least' problems add cases or use total minus unwanted.
Step-by-step method
- Decide that order doesn't matter.
- Split into parts (e.g. men and women).
- Multiply combinations for each part; add separate cases.
Worked example 1 (Basic)
In how many ways can 2 students be chosen from 6?
- 6C2 = 15
- Answer: 15
Worked example 2 (Standard)
A committee of 3 men and 1 women is chosen from 8 men and 4 women. How many ways?
- 8C3 × 4C1 = 56 × 4
- = 224
- Answer: 224
Worked example 3 (Challenge)
A team of 3 is chosen from 7 men and 5 women. In how many ways does it include at least one man?
- Total 12C3 = 220
- All women 5C3 = 10
- At least one man = 210
- Answer: 210
Common mistakes and misconceptions
- Using permutations
- Adding where you should multiply
Practice questions
- (Basic) In how many ways can 2 students be chosen from 12?
- (Basic) In how many ways can 2 students be chosen from 11?
- (Standard) A committee of 1 men and 3 women is chosen from 7 men and 7 women. How many ways?
- (Standard) A committee of 2 men and 3 women is chosen from 7 men and 6 women. How many ways?
- (Challenge) A team of 3 is chosen from 8 men and 6 women. In how many ways does it include at least one man?
- (Challenge) A team of 3 is chosen from 8 men and 8 women. In how many ways does it include at least one man?
Answer key with full working
- Q1: 12C2 = 66 → Answer: 66
- Q2: 11C2 = 55 → Answer: 55
- Q3: 7C1 × 7C3 = 7 × 35 → = 245 → Answer: 245
- Q4: 7C2 × 6C3 = 21 × 20 → = 420 → Answer: 420
- Q5: Total 14C3 = 364 → All women 6C3 = 20 → At least one man = 344 → Answer: 344
- Q6: Total 16C3 = 560 → All women 8C3 = 56 → At least one man = 504 → Answer: 504
Syllabus note
This skill is listed under "Permutations and Combinations" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is selections and committees in?
"Permutations and Combinations", Class 11 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.