Let a word be a sequence of letters regardless of whether it

Let a \'word\' be a sequence of letters, regardless of whether it is in the dictionary or not. How many 10-letter words are there using 5 different vowels and 5 different consonants?

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Solution

vowels=5 out of 5 vowels

consonants=5 out of 21 consonants

number of 10-letter words are there using 5 different vowels and 5 different consonants = 5c5 *21c5

number of 10-letter words are there using 5 different vowels and 5 different consonants = 1* 21!/((21-5)!*5!)

number of 10-letter words are there using 5 different vowels and 5 different consonants = (21*20*19*18*17)/(5*4*3*2*)

=2441880/120

=20349words