Q

# Tell me? The number of selections of four letters from the letters of the word ASSASSINATION is

The number of selections of four letters from the letters of the word ASSASSINATION is

• Option 1)

72

• Option 2)

71

• Option 3)

66

• Option 4)

52

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As learnt in concept

Theorem of Combination -

Each of the different groups or selection which can be made by taking r things from n things is called a combination.

$^{n}c_{r}=\frac{(n)!}{r!(n-r)!}$

- wherein

Where $1\leq r\leq n$

The Number of ways of Arrangement of objects -

The number of ways of n different objects taken all at a time $=\ ^{n}p_{n}=n!$

- wherein

Where 0! = 1

Case I All letters different

$6P_{4}=360$

Case II Only 2 letters are same

$_{C_{1}}^{4}\times_{C_{2}}^{5}\times\frac{4!}{2!}=480$

Case III 2 letters repeated twice

$_{C_{2}}^{4}\times\frac{4!}{2!2!}=36$

Case IV Only 3 letters are same $_{C_{1}}^{2}\times_{C_{1}}^{5}\times4=40$

Case V All letters same =1 case

Total =360+480+36+40+1=917

Option 1)

72

This is correct option

Option 2)

71

This is incorrect option

Option 3)

66

This is incorrect option

Option 4)

52

This is incorrect option

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