Vidaara.orgClass 11 · Mathematics
CodeVID-M11-06-COM-01
Combinations — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
$ {}^{n}C_{r}=$
- A.$\dfrac{n!}{(n-r)!}$
- B.$\dfrac{n!}{r!(n-r)!}$
- C.$n!\,r!$
- D.$\dfrac{n!}{r!}$
2.
$ {}^{6}C_{2}=$
- A.$12$
- B.$15$
- C.$30$
- D.$36$
3.
$ {}^{n}C_{n}=$
- A.$0$
- B.$1$
- C.$n$
- D.$n!$
4.
$ {}^{7}C_{5}=$
- A.$21$
- B.$35$
- C.$42$
- D.$7$
5.
$ {}^{10}C_{8}=$
- A.$45$
- B.$90$
- C.$80$
- D.$10$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Evaluate $ {}^{8}C_{3}$.
7.
Evaluate $ {}^{10}C_{2}$.
8.
Find $r$ if $ {}^{6}C_{r}=15$.
9.
Evaluate $ {}^{9}C_{0}+{}^{9}C_{9}$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
From $8$ players, in how many ways can $5$ be chosen?
11.
In how many ways can a committee of $3$ be formed from $10$ people?
12.
How many diagonals does a hexagon have?
13.
From $5$ men and $4$ women, in how many ways can a committee of $3$ with exactly $2$ men be formed?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
From $7$ men and $5$ women, a committee of $5$ is to be formed with at least $3$ women. In how many ways?
15.
In how many ways can a student choose $5$ questions out of $9$ if $2$ are compulsory?
Answer Key
Section A — Multiple Choice Questions
- (B) $\dfrac{n!}{r!(n-r)!}$
- (B) $15$
- (B) $1$
- (A) $21$
- (A) $45$
Section B — Short Answer (2 marks)
- $56$.
- $45$.
- $r=2$ or $r=4$.
- $2$.
Section C — Short Answer (3 marks)
- $56$.
- $120$.
- $9$.
- $40$.
Section D — Long Answer (5 marks)
- $246$.
- $35$.
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