# How To Solve Quickly Permutation Combination

## How to Solve Permutation and Combination Questions Quickly.

Permutation is an arrangement of objects in a definite order.

• Number of all permutations of n things, taken r at a time, is given by
nPr = n!/(n-r)!

Combination is selection of objects where order does not matter.

• Number of all combinations of n things, taken r at a time, is given by
nCr = n!/(r!) (n-r)!

Here we can easily understand how to solve permutation and combination easy. ## Type 1: How to Solve Quickly Permutation and Combination Different ways to arrange (with repetition)

### Question 1.

How many 3 letter words with or without meaning can be formed out of the letters of the word MONDAY when repetition of words is allowed?
Options:
A. 125
B. 216
C. 120
D. 320

#### Solution:

6 * 6 * 6 = 216
OR
We can solve directly by formula nr = 63 = 216

### Question 2.

In how many ways the letters in the word TOOTH can be arranged?
Options:
A. 120
B. 40
C. 20
D. 30

#### Solution:

5!/2! * 2!
= 5 * 4 * 3 * 2 * 1 / 2 * 1 * 2 * 1
= 120 / 4
= 30

### Question 3.

How many three digit numbers can be formed using digits 2, 3, 4, 7, 9 so that the digits can be repeated.
Options:
A. 125
B. 360
C. 24
D. 6

#### Solution:

Each place can be filled by any one of 5 digits
Total numbers = 5 * 5 *5 =125
OR
We can solve directly by formula nr = 53 = 125

## Type 2: Different ways to arrange (without repetition)

### Question 1.

How many five letter words with or without meaning, can be formed from the word ‘COMPLEXIFY’, if repetition of letters is not allowed?

Options:
A. 43200
B. 30240
C. 12032
D. 36000

#### Solution:

10P5 = 10!/ (10 – 5)! = 10 * 9 * 8 * 7 * 6 = 30240

### Question 2.

In how many different ways can the letters of the word ‘LOGARITHMS’ be arranged so that the vowels always come together?

Options:
A. 6720
B. 241920
C. 40320
D. 360344

#### Solution:

In such questions we treat vowels as one letter.
So the word becomes LGRTHMS (OAI)
It means there are total 8 letters. Therefore, number of ways of arranging these letters = 8! = 40320
Now, there are three vowels (OAI), number of ways of these letters can be arranged = 3! = 6
Required number of words = 40320 * 6 = 241920

### Question 3.

How many three digit numbers can be formed from the digits 3, 4, 5, 7, 8, and 9. Also, the number formed should be divisible by 5 and no repetition is allowed?

Options:

A. 20
B. 24
C. 25
D. 10

#### Solution:

The number which is divisible by 5 has 5 or 0 at one’s place. In this case we must have 5 at the unit place as 0 is not in the list.
There are total 6 digit out of which last digit is fixed by 5. Therefore, we are left with 5 digits (3, 4, 7, 8, 9) at the tens place. Similarly, the hundred place can be filled by 4 digits.
So, required number = 4 * 5 * 1 = 20

## Type 3: How To Solve Permutation and Combination Question- (with repetition)

### Question 1.

An ice cream seller sells 5 different ice-creams. John wants to buy 15 ice creams for his friends. In how many ways can he buy the ice-cream?
Options:
A. 1450
B. 3768
C. 3876
D. 1540

#### Solution:

r + n -1Cr = 15 + 5 – 1C15 =19C15
We know that, nCr = n!/(r!) (n-r)!
19C15 = 19!/15! (19 – 15)! = 3876

### Question 2.

There are 5 types of soda flavor available in a shop. In how many ways can 10 soda flavors be selected?
Options:
A. 1454
B. 1001
C. 1211
D. 1540

#### Solution:

r + n – 1Cr = 10 + 5 – 1C10 = 14C10
We know that, nCr = n!/(r!) (n-r)!
14C10 = 14!/10! * (14 -10)! = 1001

### Question 3.

In how many ways can 16 identical toys be divide in 4 children?
Options:

A. 966
B. 696
C. 969
D. 996
Correct option: C

#### Solution:

r + n – 1Cr = 16 + 4 – 1C16 = 19C16
We know that, nCr = n1/(r!) (n-r)!
19C16 = 19!/16! * (19 -16)! = 969

## Type 4: Permutation and Combination Solve Question Quickly. (without repetition)

### Question 1.

A wooden box contains 2 grey balls, 3 pink balls and 4 green balls. Fins out in how many ways 3 balls can be drawn from the wooden box. Make sure that at least one pink ball is included in the draw?
Options:
A. 64
B. 46
C. 56
D. 65

#### Solution:

According to the question, we have, (one pink and two non-pink balls) or (two pink and one non-pink balls) or (3 pink)
Therefore, required number of ways are (3C1 * 6C2) + (3C2 * 6C1) + (3C3) = 45 +18 + 1 = 64

### Question 2.

There are 5 boys and 10 girls in a classroom. In how many ways teacher can select 2 boys and 3 girls to make a dance group?
Options:
A. 720
B. 1200
C. 240
D. 840

#### Solution:

Required numbers of ways = 5C2 * 10C3 = 10 * 120 = 1200

### Question 3.

There are 10 consonants and 5 vowels. Out of which how many words of 5 consonants and 2 vowels can be made?
Options:
A. 2520
B. 1200
C. 210
D. 720

#### Solution:

Number of ways of selecting (5 consonants out of 10) and (2 vowels out of 4) = 10C5 * 5C2 = 252 * 10 = 2520

### 2 comments on “How To Solve Quickly Permutation Combination”

• Prakash Kumar

these questions are really helps to understands the each and every concepts thank you prep ins teams keep it up 5 0
• Nishu Sagar

welcome Prakash Kumar 0 0