# Permutation & Combination

### The number of parallelograms that can be formed

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of four parallel lines, is

1. 18
2. 24
3. 32
4. 36

### How many numbers with two or more digits can be formed

How many numbers with two or more digits can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, so that in every such number, each digit is used at most once and the digits appear in the ascending order?

### A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them

A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers?

1. 6666666
2. 6666600
3. 6666660
4. 6666000

### A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them

A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees?

1. 80
2. 160
3. 200
4. 320

### Consider the five points comprising of the vertices of a square and the intersection point of its diagonals

Consider the five points comprising of the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points?

1. 4
2. 6
3. 8
4. 10

### Boxes numbered 1, 2, 3, 4 and 5 are kept in a row, and they which are to be filled

Boxes numbered 1, 2, 3, 4 and 5 are kept in a row, and they which are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects?

1. 8
2. 10
3. 15
4. 22

### How many five-digit numbers can be formed using the digits 2, 3, 8, 7, 5 exactly

How many five-digit numbers can be formed using the digits 2, 3, 8, 7, 5 exactly once such that the number is divisible by 125?

1. 0
2. 1
3. 3
4. 4

### In a six-node network, two nodes are connected to all the other nodes

In a six-node network, two nodes are connected to all the other nodes. Of the remaining four, each is connected to four nodes. What is the total number of links in the network?

1. 7
2. 13
3. 15
4. 26

### In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table

In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the the vice chairman and a director?

1. 9! × 2
2. 2 × 7!
3. 2 × 8!
4. 2 × 6!

### Let S be the set of five-digit numbers formed by digits 1, 2, 3, 4 and 5

Let S be the set of five-digit numbers formed by digits 1, 2, 3, 4 and 5, using each digit exactly once such that exactly two odd position are occupied by odd digits. What is the sum of the digits in the rightmost position of the numbers in S?

1. 192
2. 216
3. 228
4. 294

### Ten points are marked on a straight-line and 11 points are marked on another straight-line

Ten points are marked on a straight-line and 11 points are marked on another straight-line. How many triangles can be constructed with vertices from among the above points?

1. 495
2. 550
3. 1045
4. 2475

### There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2

There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?

1. 144
2. 180
3. 192
4. 360

### What is the number of distinct terms in the expansion of (a + b + c)^20

What is the number of distinct terms in the expansion of (a + b + c)20?

1. 210
2. 231
3. 242
4. 253

### During the essay writing stage of MBA admission process in a reputed B-School

During the essay writing stage of MBA admission process in a reputed B-School, each group consists of 10 students. In one such group, two students are batch mates from the same IIT department. Assuming that the students are sitting in a row, the number of ways in which the students can sit so that the two batch mates are not sitting next to each other, is

1. 3540340
2. 2874590
3. 2903040
4. None of the above

### In the board meeting of a FMCG Company, everybody present in the meeting shakes hand with everybody else

In the board meeting of a FMCG Company, everybody present in the meeting shakes hand with everybody else. If the total number of handshakes is 78, the number of members who attended the board meeting is

1. 7
2. 9
3. 11
4. 13

### If a 4 digit number is formed with digits 1, 2, 3 and 5. What is the probability

If a 4 digit number is formed with digits 1, 2, 3 and 5. What is the probability that the number is divisible by 25, if repetition of digits is not allowed?

1. 1/12
2. 1/6
3. 1/8
4. 1/4