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 1 trainees and 4 engineers be included in a committee

If 1 trainees and 4 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 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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Direction: Study the given information carefully and answer the questions that follow—

A store contains 3 red, 4 blue, 4 green and 4 whites’ bats.

If two bats are picked at random, what is the probability that both are white?

Probabilities if both are White

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If four bats are picked at random, what is the probability that two are blue and two is green?

**A. ** 12/455

**B. ** 35/355

**C. ** 18/455

**D. ** 18/35

**E. ** None of these

**Answer : ****Option A**

**Explaination / Solution: **

Probability if two are Blue and two are Green =

[(^{4}C_{2}*^{4}C_{2})/^{15}C_{4}] = (6*6)/1365 → 12/455

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If three bats are picked at random, what is the probability that at least one is green?

**A. ** 2/5

**B. ** 60/65

**C. ** 44/455

**D. ** 58/91

**E. ** None of these

**Answer : ****Option D**

**Explaination / Solution: **

Probability if at least one is green

[1-(^{11}C_{3}/^{15}C_{3})] = [1-(165/455)] → 58/91

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If two bats are picked at random, what is the probability that either both are red or both are white?

**A. ** 3/5

**B. ** 3/35

**C. ** 14/25

**D. ** 4/105

**E. ** None of these

**Answer : ****Option B**

**Explaination / Solution: **

Probabilities if both either are Red or either are White

(^{3}C_{2} + ^{4}C_{2})/^{15}C_{2} = (3 + 6)/105 → 3/35

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If two bats are picked at random, what is the probability that none is white?

**A. ** 8/21

**B. ** 11/21

**C. ** 13/55

**D. ** 11/22

**E. ** None of these

**Answer : ****Option B**

**Explaination / Solution: **

Probabilities if none are white

[^{11}C_{2}/^{15}C_{2}] = (55)/(105) = 11/21

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