Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

Out of 5 women and 4 men a committee of three members is to be formed in such a way that at least one member is a woman. In how many different ways can it be done?

A) 80
B) 84
C) 76
D) 96

Correct Answer:

A) 80

Description for Correct answer:
The committee will be formed as follows:

(i) 1 woman and 2 men

(ii) 2 women and 1 man

(iii) 3 women

Therefore, Required number of committees

= \( \Large ^{5}C_{1} \times ^{4}C _{2} + ^{5}C_{2} \times ^{4}C_{1} + ^{5}C_{3} \)

= \( \Large 5 \times \frac{4 \times 3}{1 \times 2} + \frac{5 \times 4}{1 \times 2} \times 4 + \frac{5 \times 4 \times 3}{1 \times 2 \times 3} \)

= 30 + 40 + 10 = 80

Part of solved Permutation and combination questions and answers : >> Aptitude >> Permutation and combination

Comments

Similar Questions

1). In how many different ways can the letters of the word TOTAL be arranged?

A). 120

B). 60

C). 48

D). 72

2). A school team has eight volleyball players. A five-member team will be selected out of these eight players. How many different selections can be made?

A). 224

B). 112

C). 56

D). 88

3). . In how many different ways can the letters of the word 'AWARE' be arranged?

A). 150

B). 120

C). 40

D). 60

4). In how many different ways can the letters of the word 'OFFICES' be arranged?

A). 2520

B). 5040

C). 1850

D). 1680

5). In how many different ways can the letters of the word 'TRUST' be arranged?

A). 60

B). 240

C). 120

D). 25

6). In how many different ways can the letters of the word ATTEND be arranged?

A). 60

B). 120

C). 240

D). None of these

7). In how many different ways can the letters of the word 'BANKING' be arranged?

A). 5040

B). 2540

C). 5080

D). 2520

8). In how many different ways can the letters of the word 'PEANUT' be arranged?

A). 720

B). 360

C). 650

D). 700

9). The Committee should consist of 2 students, 2 teachers and 1 sports coach?

A). 25

B). 64

C). 9

D). 36

10). Any five people can be selected?

A). 126

B). 45

C). 120

D). 24