Question

The number of ways in which any four letters can be selected from the word 'CORGOO' is_______.

• A. 15
• B. 11
• C. 7
• D. 720

Answer 1

The correct option is C

7

Four letters can be selected in the following ways i.e. C, O, R, G

Case (i) All different .

Case (ii) 2 like and 2 different, 2 from O and 1 from R, G and C.

Case (iii) 3 like and 1 different, 3 from O and 1 from R, G and C.

The number of ways in (i) is ${}^4{C}_4$ = 1

The number of ways in (ii) is $1{\times }^3{C}_2$ = 3

The number of ways in (iii) is $1{\times }^3{C}_1$ = 3

Therefore, required number of ways = 7.