If two shirts are picked at random, what is the probability that at most one is blue,?

**A. ** 24/25

**B. ** 17/39

**C. ** 34/39

**D. ** 11/13

**E. ** None of these

**Answer : ****Option C**

**Explaination / Solution: **

Probabilities if at most one is blue =

[(^{5}C_{0}*^{8}C_{2}+ ^{5}C_{1}*^{8}C_{1})/ ^{13}C_{2}] = (1*28 + 5*8)/(78) = 34/39

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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

Number of ways when women are majority in committee =

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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

Number of Ways when if at least 5 men include in committee = ^{7}C_{5}*^{6}C_{5}+^{7}C_{6}*^{6}C_{4}+^{7}C_{7}*^{6}C_{3}

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

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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

Number of ways when men are majority in committee = ^{7}C_{6}*^{6}C_{4}+^{7}C_{7}*^{6}C_{3}

7*35+1*20 = 125

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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

If 6 men and 4 women include in committee =

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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

If 5 men and 5 women include in committee =

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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

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

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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

If 2 trainees and 3 engineers include in committee

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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

If at least 2 trainees include in committee

= 405

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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

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

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