How many five letter words (may or may not have dictionary
meaning) can be formed from the letters of the word “EQUATION’?
How many of these will have 3 vowels and 2 consonants?
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There are 5 vowels and 3 consonants in the word 'EQUATION'. Three vowels out of 5 and 2 consonants out of 3 can be chosen in
ways. So, there are
groups each containing 3 consonants and two vowels. Now, each group contains 5 letters which are to be arranged in such a way that 2 consonats occur together. Considering 2 consonants as one letter we have 4 letters which can be arranged in 4! ways. But two consonants can be put together in 2! ways. Therefore, 5 letters in each group can be arranged in
ways.
Required number of words
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