Probability and Statistics - Online Test

Q1.

Direction: Study the following information carefully and answer the questions that follow:

A committee of 10 persons is to be formed from 7 men and 6 women

In how many ways of these committee the women are in majority

Answer : Option B
Explaination / Solution:

Number of ways when women are majority in committee = 6C6*7C4 = 1*35 = 35

Q2.

Direction: Study the following information carefully and answer the questions that follow:

A committee of 10 persons is to be formed from 7 men and 6 women

In how many ways this can be done if at least 5 men to have to be included in a committee

Answer : Option A
Explaination / Solution:

Number of Ways when if at least 5 men include in committee = 7C5*6C5+7C6*6C4+7C7*6C3

21*6+7*15+1*20 = 251

Q3.

Direction: Study the following information carefully and answer the questions that follow:

A committee of 10 persons is to be formed from 7 men and 6 women

In how many of these committee the men are in majority

Answer : Option D
Explaination / Solution:

Number of ways when men are majority in committee = 7C6*6C4+7C7*6C3

7*35+1*20 = 125

Q4.

Direction: Study the following information carefully and answer the questions that follow:

A committee of 10 persons is to be formed from 7 men and 6 women

In how many ways this can be done if 6 men and 4 women be included in a committee

Answer : Option A
Explaination / Solution:

If 6 men and 4 women include in committee = 7C6*6C4 --> 7*15 --> 105

Q5.

Direction: Study the following information carefully and answer the questions that follow:

A committee of 10 persons is to be formed from 7 men and 6 women

In how many ways this can be done if 5 men and 5 women be included in a committee

Answer : Option D
Explaination / Solution:

If 5 men and 5 women include in committee = 7C5*6C5 --> 21*6 = 126

Q6.

Direction: Study the following information carefully and answer the questions that follow:

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.

In how many ways this can be done if at least 3 trainees to have to be included in a committee

Answer : Option D
Explaination / Solution:

Number of Ways when if at least 3 trainees include in committee =

3C3*10C2 = 1*45 --> 45

Q7.

Direction: Study the following information carefully and answer the questions that follow:

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.

In how many ways this can be done if 2 trainees and 3 engineer to have to be included in a committee

Answer : Option B
Explaination / Solution:

If 2 trainees and 3 engineers include in committee

3C2*6C3 = 3*20 --> 60

Q8.

Direction: Study the following information carefully and answer the questions that follow:

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.

In how many ways this can be done if at least 2 trainees to have to be included in a committee

Answer : Option D
Explaination / Solution:

If at least 2 trainees include in committee

3C2*10C3 + 3C3*10C2 = 3*120+1*45

= 405

Q9.

Direction: Study the following information carefully and answer the questions that follow:

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.

In how many ways this can be done if 3 engineers and 2 professors or 2 trainees and 3 professor be included in a committee

Answer : Option C
Explaination / Solution:

If 3 engineers and 2 professors or 2 trainees and 3 professors include in committee

6C3*4C2 + 3C2*4C3 = 20*6 + 3*4 = 120 + 12 = 132

Q10.

Direction: Study the following information carefully and answer the questions that follow:

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.

In how many ways this can be done if 1 trainees and 4 engineers be included in a committee

Answer : Option A
Explaination / Solution:

If 1 trainees and 4 engineers include in committee
3C1*6C4 = 3*15 --> 45