How many four letter words can be formed using the letters of the word 'PANTHER', if it is given tha

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04 Feb 2022 Permutation & Combination

How many four letter words can be formed using the letters of the word 'PANTHER', if it is given that the four letter word contains alphabets T and H paired together, with T coming before H and repetition of alphabets is not allowed?

OPtion

1) 72
2) 90
3) 60
4) 75
5) 45
6) 80
7) 120
8) 150
9) 180
10) None of these

Solution

Out of the 4 letters, at two consecutive places T & H can be placed as TH _ _, _ TH _, _ _ TH, so number of ways = 3
As two letters out of 7 have been used, we have 5 letters left for the 2 left places. So, remaining two places can be arranged in 5P2 = 5 x 4 = 20 ways (without repetition)
The number of ways to make 4 letter words = 3 x 20 = 60

Correct Option: 3 Best Solution (0)