Question

In how many ways can be letters of word MULTIPLE be arranged without changing the order of the vowels.

Answer 1

Total letters in MULTIPLE = 8

(L is repeated)

So total arrangements = 8P8 / 2!
_________________

Number of vowels = 3

total ways of arranging the vowels = 3! = 6

Among the 6 ways, there is only 1 way in which the order of the vowels is maintained.
________

So only 1/6 of the total arrangements(8P8 / 2! ) will have the vowels in the same order.

So required number of arrangements = 8! / (2! × 6) = 8×7×5×4×3 = 3360

Answer 2

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Total letters in MULTIPLE = 8

(L is repeated)

So total arrangements = 8P8 / 2!

_________________

Number of vowels = 3

total ways of arranging the vowels = 3! = 6

Among the 6 ways, there is only 1 way in which the order of the vowels is maintained.

________

So only 1/6 of the total arrangements(8P8 / 2! ) will have the vowels in the same order.

So required number of arrangements = 8! / (2! × 6) = 8×7×5×4×3 = 3360.

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