Question

How many 4 letter words may be formed by using the letters of the word "assassination"?

Answer 1

Given:

The word "assassination"

To find:

How many 4 letter words may be formed by using the letters of the word "assassination"?

Solution:

From given, we have,

The word "assassination"?

Case 1: All four letters are different

6P4=360 (6 distinct characters)

Case 2: Only 2 letters are same

4C1.5C2.4!2!=480 (for repetition we can choose any one from A, S, N, I and then permute the 4 with 2 repetitions)

Case 3: 2 letters are repeated twice (like AASS)

4C2.4!2!.2!=36

Case 4: Only 3 letters are same

2C1.5C1.4=40

Case 5: All 4 letters are same

1 (only SSSS)

So, in total 360 + 480 + 36 + 40 + 1 = 917

In 917 ways the 4 letter words may be formed by using the letters of the word "assassination"