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Question
Number of four letter word can be formed using the letter of word MIRACLE if letter M is always to be included, are
Number of four letter word can be formed using the letter of word MIRACLE if letter M is always to be included, are
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Solution
The correct option is C 480
Total no. of different letters in the word 'MIRACLE' =7Total number of four letter word can be formed =7P4Total no. of different letters in the word 'MIRACLE' if 'M' is always excluded =6
Total no. of four letter word if 'M' is always excluded =6P4Therefore,Total no. of four letter word if 'M' is always included =7P4−6P4
As we know that,nPr=n!(n−r)!Therefore,Total no. of four letter word if 'M' is always included =7!3!−6!2!=840−360=480
Hence total number of four letter word can be formed using the letter of word 'MIRACLE' if letter 'M' is always to be included, are 480.
Total no. of different letters in the word 'MIRACLE' =7
Total number of four letter word can be formed =7P4Total no. of different letters in the word 'MIRACLE' if 'M' is always excluded =6
Total no. of four letter word if 'M' is always excluded =6P4
Therefore,
Total no. of four letter word if 'M' is always included =7P4−6P4
As we know that,
nPr=n!(n−r)!
Therefore,
Total no. of four letter word if 'M' is always included =7!3!−6!2!=840−360=480
Hence total number of four letter word can be formed using the letter of word 'MIRACLE' if letter 'M' is always to be included, are 480.
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