Question

How many four letter words can be formed using the word ineffective?

Answer 1

Answer:

Explanation:

Total (3e, 2f, 2i(3e,2f,2i rest 4 all different) i.e. 7 types.

(i) Al different {^6P}_4 = 6 \times 5 \times 4 \times 3 = 360  

6

P  

4

​  

=6×5×4×3=360 .

(ii) Two different, two alike.

{^2C}_1 \times {^5C}_2 \times \dfrac{4!}{2!} = 240  

2

C  

1

​  

×  

5

C  

2

​  

×  

2!

4!

​  

=240

(iii) 3 alike, 1 different  

{^1C}_1 \times {^5C}_1 \times \dfrac{4!}{3!} = 20  

1

C  

1

​  

×  

5

C  

1

​  

×  

3!

4!

​  

=20

(iv) 2 alike of one type and 2 alike of other type.

{^2C}_2 \times \dfrac{4!}{2!2!} = 6  

2

C  

2

​  

×  

2!2!

4!

​  

=6.

\therefore∴ Total number of words = 360 + 240 + 20 + 6 = 626=360+240+20+6=626.