Topics

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

A committee of 3 members is to be formed out of 3 men and 4 women. In how many different ways can it be done so that at least one member is a woman?

A) 34
B) 12
C) 30
D) 36

Correct Answer:

A) 34

Description for Correct answer:
The committee can be formed in the following ways;

(i) By selecting 2 men and 1 woman

(ii) By selecting 1 man and 2 women

(iii) By selecting 3 women

Therefore, Total number of ways of forming the committee

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

= \( \Large 3 \times 4 + 3 \times 6 = 4 \)

= 12 + 18 + 4 = 34

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

Comments

Similar Questions

1). 4 boys and three girls are to be seated in a row in such a way that no two boys sit adjacent to each other. In how many different ways can it be done?

A). 5040

B). 30

C). 144

D). 72

2). How many different words can be formed with the letters of the word 'ALLAHABAD'?

A). 7500

B). 7560

C). 7510

D). 7580

3). The committee should have all 4 professors and 1 research associate or all 3 trainees and 2 professors?

A). 12

B). 13

C). 24

D). 52

4). The committee should have 2 trainees and 3 research associates?

A). 15

B). 45

C). 60

D). 9

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

A). 720

B). 5040

C). 2520

D). 40320

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

A). 64

B). 40320

C). 960

D). 20160

7). In how many different ways can it be done so that the committee has at least one woman?

A). 210

B). 225

C). 195

D). 185

8). In how many different ways can it be done, so that the committee has at least 2 men?

A). 210

B). 225

C). 195

D). 185

9). In how many ways this can be done if at least 5 women have to be included in a committee?

A). 6000

B). 6010

C). 6062

D). 6005

10). In how many of these committees, the women are in majority?

A). 2000

B). 2700

C). 2705

D). 2702