Q.

The letters D, G, I, I and T can be used to form 5-letter strings such as DIGIT or DGIIT. Using these letters, how many 5-letters strings can be formed in which the two occurrences of the letter I are separated by at least one other letter?

A. 12

B. 18

C. 24

D. 36

E. 48

D. 36

D, I, I, G, T

Total possible arrangements of the 5 letters is given below

5!/2! = 60

Cases where the “I”s are together = 4! = 24

So, 60 – 24 = 36

OR

Arrange D, G, T first and then place “I”s.

D, G, T can be arranged in 3! = 6 ways

4 spaces are created. The “I”s need two places, so total ways = ā“Cā‚‚ = 6 ways

Total ways = 6Ɨ6 = 36