Question

The number of selections of 4 letters of the word assassination

Answer 1

13C4/4!3!2! as s comes 4 times a comes 3 time I 2 time

Answer 2

The number of selections of 4 letters of the word assassination is 66

Solution:

Given that,

A S S A S S I N A T I O N

To find: number of selections of 4 letters of the word assassination

But here, we have repeated letters

We have,

3 A's

4 S's

2 I

2 N

1 T

1 O

CASE 1: ALL 4 LETTERS ARE SAME

ways = 1

CASE 2 : 3 LETTER SAME AND 1 DIFFERENT

$2C_1 \times 5C_1 = 10$

CASE 3: 2 LETTER SAME AND 2 DIFFERENT

$4 \times 5C_2 = 40$

CASE 4 : ALL FOUR DIFFERENT LETTERS

$6C_4 = 15$

Thus,

Total = 1 + 10 + 40 + 15 = 66

Thus number of selections of 4 letters of the word assassination is 66

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