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

how to solve combination question quickly

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 = 8!/3! (8 – 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, 

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

Correct option: A

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