Question

The letters of the word 'FORTUNATES' are arranged at random in a row. What is the chance that the two 'T' come together.

Answer 1

There are 10 letters in the word ‘FORTUNATES’, which can be arranged in 10! ways.
There are two T's in the word.
Let us consider these two letters in the word ‘FORTUNATES’ as one letter.
So, when the two T's are clubbed together, we have (T,T) FORUNAES.
We can arrange 9 letters in a row in 9! ways.
Also, the two T's can themselves be arranged in 2! ways.
Hence, required probability = \[\frac{9! \times 2!}{10!} = \frac{9! \times 2}{10 \times 9!} = \frac{1}{5}\]