Asked by Kaur

The number of ways in which the letters of the word MULTIPLE be arranged without changing the order of the vowels is

Answers

Answered by oobleck
There are 3 vowels, so the 5 consonants can be divided into groups of
0,0,0,5
0,0,1,4
0,0,2,3
...
5,0,0,0
For each of those groups i,j,k,l the consonants can be permuted in
i! * j! * k! * l! ways
Then divide by 2, since the 2 L's are indistinguishable.

Maybe someone else can think of a simpler way.
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