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QUESTION
Q
In how many ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together...
Solution
SOLUTION 1:
The word THERAPY consists of 7 distinct letters with two vowels A and E.
The 5 consonants can be arranged in 5! ways and the remaining 2 vowels can be arranged in the gaps so that the vowels do not come together.
_ T_H_R_P_Y_
There are 6 gaps in between the consonants and the two vowels can be arranged in 6 gaps in 6P2 ways.
Therefore,
Total ways in which the letters of the word ‘THERAPY’ be arranged so...
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