# How To Solve Combination Questions Quickly

## How to solve Combination Questions Quickly & Definitons

Combination is an arrangement of objects where order does not matter.
There are two easy methods for solving combination questions
(i) Repetition are allowed
(ii) Repetition are not allowed ## Type 1: How to Solve Combination Question (with or without repetition)

### Question 1.

There was a flock of sheep in which 6 were male sheep 5 were female sheep. Now we need to select 4 sheep to take out wool from them. In how many different ways can they be selected such that at least one male sheep should be there?

Options:
A. 1450
B. 302
C. 295
D. 154

#### Solution:

The selection can be made in following manner
(1 male sheep and 3 female sheep) or (2 male sheep and 2 female sheep) or (3 male sheep and 1 female sheep) or (4 male sheep)
Required number of ways = (6C1 * 5C3) + (6C2 * 5C2) + (6C3 * 5C1) + (6C4)
Required number of ways = (6 * 5) + (15 * 10) + (20 * 5) + 15
Required number of ways = 30 + 150 + 100 + 15
Required number of ways = 295

### Question 2.

Among a set of 5 white balls and 3 blue balls, how many selections of 5 balls can be made such that at least 3 of them are white balls.
Options:
A. 45
B. 46
C. 44
D. 40

#### Solution:

The selection can be made in following manner
(3 white ball and 2 blue ball) or (4 white ball and 1 blue ball) or (5 white ball)
5C3 * 3C2 + 5C4 * 3C1 + 5C5
= (10 * 3) + (5 * 3) + 1
= 30 + 15 + 1
= 46

## How To Solve Quickly Combination Questions

### Question 3.

There are 7 consonants and 4 vowels. Find out how many words of 3 consonants and 2 vowels can be formed?
Options:
A. 120
B. 102
C. 20
D. 210

#### Solution:

Number of ways of selecting 3 consonants from 7= 7C3
Number of ways of selecting 2 vowels from 4= 4C2
Number of ways of selecting 3 consonants from 7 and 2 vowels from 4 = 7C3 × 4C2
= 35 * 6 = 210

### Question 4.

In how many ways can a team of 5 cricketers can be formed out of a total of 10 cricketers such that two particular cricketers should be included in each team?
Options:
A. 66
B. 65
C. 56
D. 22

#### Solution:

Two particular cricketers should be included in each team. Therefore, select remaining 5-2=3 cricketers from 10-2=8 cricketers = 8C3
8C3 = 8!/3! (8 – 3)! = 56

### Question 5.

There are 3 types of t-shirts available in a clothing store. In how many ways can 5 t-shirts be selected?
Options:
A. 21
B. 42
C. 5
D. 12

#### Solution:

r + n – 1Cr5 + 3 – 1C15 = 7C5

We know that,

nCr = n!/(r!) (n-r)!
7C5 = 7!/5! * (7 -5)! = 21