Question

Which is the maximum number of consecutive vowels to be found in an English word? Give the number and word?

Answer 1

The number of arrangements with 3 consecutive vowels is correctly explained in the original post: the number is 15120.

To find the number of arrangements with at least two consecutive vowels, we duct tape two of them together (as in the original post) and arrive at 120960.

The problem with this calculation is that every arrangement with 3 consecutive vowels was double counted: once as VV¯¯¯¯¯¯¯¯V and again as VVV¯¯¯¯¯¯¯¯. To compensate for this we must subtract 15120. The correct number of arrangements with at least two consecutive vowels is 120960−15120=105840.

Therefore, correct number of arrangements with exactly two consecutive vowels is 105840−15120=90720.