Question

The total number of ways of formation of five letter words from the letters of the word $INDEPENDENT,$ is

• A. $4200$
• B. $3320$
• C. $3840$
• D. None of these

Answer 1

Answer: (B)

$3320$

There are 11 letters in the given word INDEPENDENT.

3 N,3 E, 2 D, I,P,T (6 types of letters)

Different possibilities of choosing five letters are:

1. All different.

No. of ways $={{}^{6}c}_5\times 5!=720$

2. 2 alike, 3 different.

No. of ways$={{}^{3}c}_1\times {{}^{5}c}_3\times \frac{5!}{2!}=1800$

3. 3 alike, 2 different.

No. of ways$={{}^{2}c}_1\times {{}^{5}c}_2\times \frac{5!}{3!}=400$

4. 2 alike, 2 alike, 1 different.

No. of ways$={{}^{3}c}_2\times {{}^{4}c}_1\times \frac{5!}{2!2!}=360$

5. 3 alike, 2 alike

No. of ways$={{}^{2}c}_1\times {{}^{2}c}_1\times \frac{5!}{3!2!}=40$

So total number of ways$=720+1800+400+360+40=3320$