# Permutation and Combination – Quiz 3

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# Permutation and Combination – Quiz 3

### Introduction

Permutation and Combination is one of important topic in Quantitative Aptitude Section. In Permutation and Combination – Quiz 3 article candidates can find questions with an answer. By solving this questions candidates can improve and maintain, speed, and accuracy in the exams. Permutation and Combination – Quiz 3 questions are very useful for different exams such as IBPS PO, Clerk, SSC CGL, SBI PO, NIACL Assistant, NICL AO, IBPS SO, RRB, Railways, Civil Services etc.

### Q1

A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
A. 150 B. 200 C. 250 D. 300

B
The number of ways to select two men and three women = $^{5}{C}_{2} \times ^{6}{C}_{3}$
= $\frac {(5 \times 4)}{(2 \times 1)}$ $\times$ $\frac {(6 \times 5 \times 4)}{(3 \times 2)}$
= 200

### Q2

What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
A. 100 B. 60 C. 30 D. 20

C
The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= $^{4}{C}_{2} \times ^{5}{C}_{1}$
= $\frac {(4 \times 3)}{(2 \times 1)}\times 5$
= 30 ways

### Q3

A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
A. 165 B. 185 C. 205 D. 225

A
Total number of persons in the committee = 5 + 6 = 11
Number of ways of selecting group of eight persons = $^{11}{C}_{8} \times ^{11}{C}_{3}$ = $\frac {(11 \times 10 \times 9)}{(3 \times 2)}$ = 165 ways

### Q4

There are 18 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
A. 200 B. 190 C. 95 D. 380

D
The total number of stations = 20
From 20 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in $^{20}{P}_{2}$ ways.
$^{20}{P}_{2}$ = 20 * 19 = 380.

### Q5

A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most -
A. 216 B. 243 C. 215 D. 729

C
Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 $\times$ 6 $\times$ 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 216 - 1 = 215.