Question

How many different permutations of 4 letters of the word earthquake are possible?​

Answer 1

Answer:

44

The maximum number of different permutation of 4 letter of the word EARTHQUAKE is 44

Answer 2

The permutation of 4 letters of the word "EARTHQUAKE "total number of ways = 2190

Step-by-step explanation:

• We are given the word "EARTHQUAKE". We are asked the different permutations of 4 letters. In this word, 2 E's and 2 A's are repeated.

• Therefore, first we have to select four letters from the word "EARTHQUAKE".

To do this, we have three possibilities.

• Case 1: All the chosen four letters are different:

• No of such types of ways =$^8C_4 \times 4!$ = 1680

• Case 2: In the chosen four letters, 2 letters are different and 2 are same.

• No of such types of ways =$\dfrac{^2C_1\times^7C_2 \times 4!}{2!}$ = 504

• Case 3: In the chosen four letters, 2 letters are same and 2 are same.

• No of such types of ways =$\dfrac{^2C_2 \times 4!}{2!\times 2!} = 6$

We can follow any one from above three. So, we add them to find out the total no of ways.

Thus, total number of ways = 1680 + 504 + 6 = 2190