In how many different ways can the letters of the word ‘TRANSPIRATION’ be arranged so that the vowels always come together?
A
2429500
B
1360800
C
1627800
D
None of these
Correct Answer: 1360800
The word ‘TRANSPIRATION’ has 13 letters in which each of T, R, A, N and I has come two timesWe have to arrange TT RR NN PS (AA II O)
There are five vowels in the given words.
∴ We consider these give vowels as one letter.
∴ Required number of arrangements
$$\eqalign{ & = \frac{{9! \times 5!}}{{2!\, 2! \,2! \,2! \,2!}} \cr & = \frac{{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 5 \times 4 \times 3 \times 2}}{{2 \times 2 \times 2 \times 2 \times 2}} \cr & = 1360800 \cr} $$
