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CBSE · Class 11 · Mathematics

Permutations and Combinations

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
The value of 6P3 is:
  1. 360
  2. 20
  3. 216
  4. 120
2.
The value of 15C5 is:
  1. 360,360
  2. 5,005
  3. 3,003
  4. 2,002
3.
How many arrangements can be made of all the letters of the word MISSISSIPPI?
  1. 69,300
  2. 17,325
  3. 39,916,800
  4. 34,650
4.
How many 2-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6, 7, if no digit is repeated?
  1. 42
  2. 49
  3. 21
  4. 14
5.
0! equals:
  1. 1
  2. undefined
  3. infinity
  4. 0
6.
In how many ways can a committee of 2 men and 3 women be chosen from 6 men and 5 women?
  1. 1,800
  2. 25
  3. 462
  4. 150
7.
(5 + 1)! ÷ (5 − 1)! equals:
  1. 30
  2. 20
  3. 6
  4. 2
8.
Assertion (A): 8C3 = 8C5.
Reason (R): Choosing r things to take is the same as choosing the n − r things to leave, so ⁿCᵣ = ⁿCn−ᵣ.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
How many arrangements of the letters of CLOUDY are there? How many of them begin with O?
10.
How many 3-digit even numbers can be formed from the digits 1 to 7, if no digit is repeated?
11.
Find n if ⁿP2 = 306.
12.
A committee of 4 is to be chosen from 8 men and 7 women. In how many ways can this be done so that there is at least one woman?
13.
In how many arrangements of the letters of ORANGE do N and G come together?
14.
If ⁿC6 = ⁿC10, find n and ⁿC2.
15.
At a meeting, each of 17 people shakes hands with every other person once. How many handshakes are there?
16.
There are 10 points in a plane, of which exactly 6 are collinear (no other three are). How many straight lines and how many triangles can be formed by joining them?
Section C — Word problems4 × 4 = 16 marks
17.
(a) How many arrangements of the letters of TOMATO are there? (b) In how many of them do all the vowels come together?
18.
A team of 4 is chosen from 9 boys and 8 girls. In how many ways can it be chosen if it must have at least 2 girls?
19.
In how many ways can 3 cards be chosen from a pack of 52 cards? In how many of these is there (a) exactly one ace, (b) at least one ace?
20.
7 boys and 6 girls stand in a row. In how many ways can they stand (a) in any order, (b) so that boys and girls alternate, (c) so that all the girls stand together?
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CBSE · Class 11 · Mathematics

Answer key

Permutations and Combinations · AW-11M-PNC-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 1206 × 5 × 4
2(c) 3,00315! ÷ (5! × 10!)
3(d) 34,65011! ÷ (repeats: I × 4, S × 4, P × 2)
4(a) 427P2
5(a) 1—
6(d) 1506C2 × 5C3
7(a) 306 × 5
8(a) Both A and R are true, and R is the correct explanation of A.A is true: 8C3 = 56 and 8C5 = 56. R is true and explains A.
9720; 1206!; fix O, then 5!
1090units digit: 3 even choices; the rest: 6P2
11n = 18n(n − 1) = 306
121,295all committees 15C4 minus all-men 8C4
13240treat NG as one block: 5! × 2!
14n = 16; 16C2 = 120ⁿCᵣ = ⁿCₛ with r ≠ s means r + s = n
1513617C2
16Lines: 31; triangles: 10010C2 − 6C2 + 1; 10C3 − 6C3
17(a) 180; (b) 36(b) treat the vowels OAO as one block: 12 arrangements of the block and the consonants, × 3 arrangements of the vowels inside it
181,5822 girls: 8C2 × 9C2 = 1,008; 3 girls: 8C3 × 9C1 = 504; 4 girls: 8C4 × 9C0 = 70
1922,100; (a) 4,512; (b) 4,80452C3; 4C1 × 48C2; 52C3 − 48C3 (hands with no ace)
20(a) 6,227,020,800; (b) 3,628,800; (c) 29,030,400(b) 7! × 6!; (c) girls as one block: 8! × 6!