# Permutation and Combination – Quiz 4

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# Permutation and Combination – Quiz 4

### Introduction

Permutation and Combination is one of important topic in Quantitative Aptitude Section. In Permutation and Combination – Quiz 4 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 4 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

The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is -.
A. ${(6!)}^{2}$ B. ${(6!)}^{2} \times ^{7}{p}_{6}$ C. 2 (6!) D. $(6!) \times 7!$

B
We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in $^{7}{p}_{6}$ ways.
Hence required number of ways = ${(6!)}^{2} \times ^{7}{p}_{6}$

### Q2

How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
A. 360 B. 60 C. 300 D. 180

A
The given digits are six.
The number of four digit numbers that can be formed using six digits is $^{6}{p}_{4}$ = 6 $\times$ 5 $\times$ 4 $\times$ 3 = 360.

### Q3

In how many ways can six members be selected from a group of ten members?
A. 4 B. $^{10}{c}_{4}$ C. 10 D. $^{7}{p}_{6}$

B
Six members can be selected from ten members in
$^{10}{c}_{6}$ = $^{10}{c}_{4}$ ways.

### Q4

In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
A. 30 B. 13 C. 40 D. 20

A
The word contains five consonants. Three vowels, three consonants can be selected from five consonants in $^{5}{c}_{3}$ ways, two vowels can be selected from three vowels in $^{3}{c}_{2}$ ways.
3 consonants and 2 vowels can be selected in $^{5}{c}_{3}$ . $^{3}{c}_{2}$ ways i.e., 10 $\times$ 3 = 30 ways.

### Q5

In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
A. 400 B. 500 C. 600 D. 20

B
We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 $\times$ 25 ways i.e., = 500 ways.