In how many ways can the letters in WONDERING be arranged with exactly two conse

Question

In how many ways can the letters in WONDERING be
arranged with exactly two consecutive vowels?

pls show your work id like to understand how you come up w/ the answer. thanks

Explanation / Answer

There are 9 distinct letters: 6 consonants and 3 vowels. i) First, arrange the 6 consonants ==> 6! ways. ii) Next, there are 3*2 = 6 ways to arrange the cluster of two consecutive vowels. iii) Among the 6+1 = 7 gaps among the consonants, we place the double vowel cluster and the third vowel in 2 of these gaps. ==> P(7,2) = 7 * 6 = 42 ways. Using (i)-(iii): There are 6! * 6 * 42 ways to arrange the letters in the word WONDERING as prescribed.

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