# How To Solve Combination Questions Quickly

## How to solve Combination Problems Quickly

How to solve Combination Questions Quickly is a frequently asked question on google, and we will be discussing the same thing over this page.

Combination Questions are mostly on the basis of finding  the number of ways of selecting the items .

Questions on Combination can be solve by formula,$\mathbf{^nC_r = \frac{n!}{(n-r)! r! }}$ ### 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
• Repetition are allowed
• 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

Correct option: C

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

Correct option: B

### 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

Correct option: D

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 = $\frac{8!}{(8-3)! 3! }$ = 56

Correct option: C

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,

$^nC_r = \frac{n!}{(n-r)! r! }$

7C5 = $\frac{7!}{(7-5)! 5! }$= 21

Correct option: A