Question 1164489: In how many different ways can the letters of the word BADMINTON be
arranged such that all consonants are always together?
Answer by greenestamps(13214)   (Show Source):
You can put this solution on YOUR website!
Since the 6 consonants are to be together, put them in a single group. That gives us 4 items to be put in some order -- the 3 vowels, and the group of 6 consonants.
Those 4 items can be arranged in 4! = 24 different ways.
Within the group of 6 consonants, or which 2 are the same, the number of arrangements is 6!/2! = 720/2 = 360.
The total number of arrangements with the 6 consonants together is then 24*360 = 8640.
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