Combi Offer #7
The English alphabet system has vowels and consonants. How many words with different vowels and different consonants can be formed from the alphabet ?
The answer is 50400.
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We choose 2 out of the 5 vowels
(5C2)
We choose 2 out of the 21 consonants
(21C2)
There are 4! ways of re-arranging the chosen letters.
Therefore, by the Multiplication Principle of Counting, the answer is (5C2)(21C2)(4!) = 50400