__Permutations and Combinations Practice Questions__
These Permutation and
Combination questions/problems with solutions provide you vital practice for
the topic. The purpose of these posts is very simple: to help you learn through
practice. Solve these problems to succeed in upcoming SBI Clerk/PO exams 2018.

**1. In how many different ways can 2 vowels and 3 consonants be selected from 4 vowels and 10 consonants?**

a) 720

b) 840

c) 620

d) 240

e) None of these

**2. Find the number of ways in which 6 players out of 11 players can be selected so as to include 3 particular players.**

a) 56

b) 54

c) 45

d) 65

e) None of these

**3. In how many ways can 3 people be seated in a row containing 6 seats?**

a) 110

b) 130

c) 140

d) 120

e) None of these

**4. How many 4 letter code can be formed using the first 9 letters of the English alphabets, if no letter can be repeated?**

a) 3024

b) 3036

c) 3021

d) 3034

e) None of these

**5. In how many different ways can the letters of the word ‘ASSASINATION’ be arranged?**

a) 1221846

b) 3234464

c) 3326400

d) 3126408

e) None of these

**6. If**

^{n}p_{4}= 10 ×^{n-1}p_{2}, find the value of n = ?
a) 5

b) 4

c) 10

d) 12

e) None of these

**7. Out of 5 men and 3 women, a committee of 3 persons is to be formed. In how many ways can it be formed selecting at least 2 women?**

a) 15

b) 16

c) 21

d) 56

e) None of these

**8. There are 35 teachers in a school. In how many different ways one principal and one vice principal can be chosen?**

a) 1190

b) 1160

c) 1170

d) 1180

e) 1090

**9. For how many integers between 10 and 100 in the tens digit equal to 5, 6 or 7 and the units digit (ones digit) equal to 2, 3, 4 ?**

a) three

b) four

c) six

d) nine

e) None of these

**10. Four boys and three girls are to be seated for a dinner such that no two girls sit together and no two boys sit together. Find the number of ways in which this can be arranged.**

a) 144

b) 36

c) 72

d) 180

e) None of these

**Solutions:**

**1. A)**Two vowels can be selected from 4 in

^{4}C

_{2}ways. Three consonants can be selected from 10 in

^{10}C

_{3}ways.

∴ 2 vowels and 3 consonants can be selected in (

^{4}C_{2}×^{10}C_{3}) ways
= (4 * 3)/(2 * 1) × (10 *
9 * 8)/(3 * 2 * 1) = 720

**2. A)**Since, 3 particular players are always included, the choice now reduces to only 3 players among 8 players which can be done in

^{8}C

_{3}ways.

^{8}C

_{3}= 8!/(3! 5!) = (8 * 7 * 6 * 5!)/(3 * 2 * 1 * 5!) = 8 * 7 = 56

**3. D)**First person can be seated in 6 ways, the second person in 5 ways and the third person in 4 ways.

Then, by fundamental
principle, total number of ways in which three persons can be seated in 6 seats
in a row is (6 × 5 × 4) ways = 120 ways

**4. A)**By fundamental principle, it is (9 × 8 × 7 × 6) ways = 3024 ways

**5. C)**‘

**ASSASINATION’**contains 12 letters which can be grouped as follows.

A = 3, S = 3, I = 2, N =
2, T = 1, O = 1

∴ Required permutations = 12!/(3! * 3! * 2!* 2!) = 3326400

**6. A)**

**7. B)**

**Case – I**

Committee contains 2
women and 1 men.

∴ No. of ways of forming this committee = (number of ways of
choosing 2 women out of 3) × (number of ways of choosing 1 man out of 5)

=

^{3}C_{2}⋅^{5}C_{1}=3 × 5 = 15**Case – II**

Committee contain 3 women
and 0 men

No. of ways of forming
this committee = number of ways of choosing 3 women out of 3.

=

^{3}C_{3 }=1
∴ Total number of ways = 15 + 1 = 16

**8. A)**Ways of choosing a principal from 35 teacher = 35.

Now, after choosing
principal, no. of ways of choosing Vice principal = 34 [∵ 35 – 1 = 34]

Hence, no of ways for
selecting a principal and a vice – principal

= 35 × 34

= 1190 way

**9. D)**For the tens place we have 3 choices.

And for the units place
we have 3 choices.

∴ Total number of integers we can form = 3 × 3 = 9

**10. A)**Since no two girls and no two boys sit together it means they sit on the alternate positions.

Therefore first of all we
arrange 3 girls in 3! ways then we arrange 4 boys in newly created 4
places in

^{4}P_{4}ways
Thus the total number of
arrangements = 3! × 4! = 144