If the letters of the word “TIRUPATI” are written down at random, then what is the probability that both Ts are always consecutive?

Correct option is B

Solution:

Let's calculate the probability that both 'T's are always consecutive when the letters of the word 'TIRUPATI' are arranged randomly.

Total arrangements of the word 'TIRUPATI':

The word has 8 letters, with 2 identical 'T's. and 2 identical I's The total number of arrangements can be calculated as:

= $$\frac{8!}{2! \times 2!} = \frac{40320}{4} = 10080$$ ​

Favorable arrangements where both 'T's are consecutive:

Treat 'TT' as a single unit. This gives us 7 units: TT, I, R, U, P, A, I. The arrangements for these 7 units are: 

​$$\frac{7!} { 2!} = \frac{5040} { 2} = 2520$$​​

Probability calculation:

The probability that both 'T's are always consecutive is given by:

Probability = $$\frac{\text{Favorable arrangements} }{\text{ Total arrangements}} = \frac{2520}{ 10080} = \frac{1}{4}$$​ 

Thus, the correct probability that both 'T's are always consecutive is $$\frac{1}{4}$$​.