Latest Others Aptitude Question SOLUTION: The number of permutations of the letters of the word LUMINARY such that niether LURY nor MINA occur together? a. 46800 b. 24680 c. 40086 d none of these

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(#M40019532) OTHERS Numerical Ability question Keep an EYE

The number of permutations of the letters of the word LUMINARY such that niether LURY nor MINA occur together?
a. 46800 b. 24680 c. 40086 d none of these

Asked In Others mohan lal garg (10 years ago)

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Jasmine Khan  (8 years ago)

If we observe there are 8 letters in the given word LUMINARY.
Now we will find the number of permutations in which either LURY or MINA occurs.
L U R Y _ _ _ _ we will fix LURY on 4 places out of 8 places. so remaining letters can be arranged on remaining places in 4! ways. And LURY can be kept on 5 places.
hence the total number of ways in which we can get LURY is 5 x 4! ways.

Similar logic for MINA.
Total number of ways in which we can get MINA is 5 x 4! ways.

Number of permutations in which LURY and MINA doesnt occur = Total number of permutations - Number of permutations i which LURY and MINA occurs

=> Number of ways in which LURY and MINA doesnt occur = 8! - (5 x 4! + 5 x 4!) = 40080 ways

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