Question
In how many different ways can the letters of the word
"AIRSTRIKE" be arranged if all the vowels must always be grouped together?Solution
The word “AIRSTRIKE’’ contains 9 letters with 4 vowels, (A, 2I, 2R, S, T, K, E)
If vowels comes together, then 4 vowels will behave as a single entity, so, remaining 5 consonants and this entity, a total of 6 letters will arrange themselves in 6! Ways, and 4 vowels will arrange themselves in
(4!/2!) Ways, as there are 2I,
So, total number of ways of arranging letters of the word ‘“AIRSTRIKE’’ such that all the vowels always come together = (6!/2!) × (4!/2!) = 360 × 12 = 4320
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