## 2nd Bank PO level Question Set, 2nd on topic Permutation and Combination

This is the 2nd question set of 10 practice problem exercise for Bank PO exams and 2nd on topic Permutation and Combination. Students must complete this question set in prescribed time first and then only refer to the corresponding solution set for gaining maximum benefits from this resource.

In MCQ test, you need to deduce the answer in shortest possible time and select the right choice.

Based on our analysis and experience we have seen that, for accurate and quick answering, the student

- must have complete understanding of the basic concepts in the topic area
- is adequately fast in mental math calculation
- should try to solve each problem using the basic and rich concepts in the specific topic area and
- does most of the deductive reasoning and calculation in his or her head rather than on paper.

Actual problem solving is done in the fourth layer. You need to use **your problem solving abilities** to gain an edge in competition.

We list below the few important formulas for permutation and combination. If you already know, you may skip.

### Basic formulas on permutation and combination

**First case:** **Permutation** (or number of possible ordered arrangements) of $r$ **distinct objects** out of $N$ distinct objects. It is,

$^NP_r=\displaystyle\frac{N\text{!}}{(N-r)\text{!}}$, where Factorial $N$, expressed as $N\text{!}$, is equal to the product of integers starting from $N$ decreasing by 1 and ending with 1.

In other words,

$N!=N\times{(N-1)}\times{(N-2)}\times{...}\times{2}\times{1}$.

With this knowledge we can express,

$^NP_r=N\times{(N-1)}\times{(N-2)}\times{...}\times{(N-r+1)}$, cancelling out $(N-r)\text{!}$ between numerator and denominator.

For example, permutation of 3 distinct objects out of 8 distinct objects will be,

$^8P_3=8\times{7}\times{6}$, the denominator $(8-3)\text{!}=5\text{!}$ is cancelled out with part of the numerator.

**Second case: ** **Permutation** of $r$ objects out of $N$ objects with $q$ objects in the set of $N$ **objects alike** or same,

$^NP_r\text{ with q alike}=\displaystyle\frac{N\text{!}}{(N-r)\text{!}\times{q\text{!}}}$.

**Third case:** **Combination or selection** of $r$ distinct objects out of $N$ distinct objects,

$^NC_r=\displaystyle\frac{N\text{!}}{r\text{!}\times{(N-r)\text{!}}}={^NC_{N-r}}$.

For more details and clear understanding of the concepts, you should refer to our extensive tutorial,

* Permutation and Combination with exercises*.

### 2nd question set - 10 problems for Bank PO exams: 2nd on topic Permutation and Combination - time 12 mins

**Problem 1.**

In how many different ways can the digits in the number "256974" be arranged using each digit only once in each arrangement such that the digits 6 and 5 are at the extreme end of the arrangements?

- 36
- 360
- 48
- 720
- None of the above

**Problem 2.**

In how many different ways can the letters of the word "CORPORATION" be arranged such that the vowels always come together?

- 840
- 8400
- 1440
- 86400
- None of the above

**Problem 3.**

A committee of 12 persons is to be formed out of 9 women and 8 men. In how of these possible committees, women will be in majority?

- 2702
- 2705
- 2000
- 2700
- None of the above

**Problem 4.**

A committee of 5 members is to be formed out of 4 students, 2 sports coaches and 3 teachers. In how many ways can the committee be formed if any 5 people can be selected?

- 45
- 120
- 24
- 126
- None of the above

**Problem 5.**

FromĀ a group of 6 men and 4 women a committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least one woman?

- 210
- 185
- 195
- 225
- None of the above

#### Problem 6.

A committee of 6 teachers is to be formed out of 5 arts teachers, 4 science teachers and 3 commerce teachers. In how many ways can the committee be formed if no teacher from the commerce stream be included in any committee?

- 81
- 46
- 62
- 84
- None of the above

**Problem 7.**

A committee of 5 members is to be formed out of 3 trainees, 6 research associates and 4 professors. In how many different ways can this be done if the committee should have all the 4 professors and 1 research associate or all 3 trainees and 2 professors?

- 15
- 12
- 19
- 25
- None of the above

**Problem 8.**

In how many different ways can the letters of the word "THERAPY" be rearranged so that the vowels never come together?

- 1440
- 720
- 5040
- 4800
- 3600

**Problem 9.**

From a group of 7 men and 6 women, 5 persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can this be done?

- 564
- 735
- 645
- 756
- None of the above

**Problem 10.**

4 boys and 3 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 this be done?

- 72
- 5040
- 144
- 30
- None of the above

You may refer to the detailed solutions in * Bank PO level Solutions 2 on Permutation Combination 2*.

### Answer to the questions

**Problem 1.** Answer: Option c: 48.

**Problem 2.** Answer: Option e: None of the above.

**Problem 3.** Answer: Option a: 2702.

**Problem 4.** Answer: Option d: 126.

**Problem 5.** Answer: Option c: 195.

**Problem 6.** Answer: Option d: 84.

**Problem 7.** Answer: Option b: 12.

**Problem 8.** Answer: Option e: 3600.

**Problem 9.** Answer: Option d: 756.

**Problem 10.** Answer. Option c: 144.

### Further reading resources

**Tutorial on Permutation and Combination with exercise problems**

**Solutions to the exercise problems on Permutation and combination**

**Bank PO level Solution set 2 on Permutation and Combination 2**

**Bank PO level Question set 2 on Permutation and Combination 2**

**Bank PO level Solutions 1 on Permutation combination 1**

**Bank PO level Question set 1 on Permutation combination 1**