The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?


There are 5 vowels and 21 consonants in English alphabets.

Choosing two vowels out of 5 would be done in 5C2 ways


Choosing 2 consonants out of 21 can be done in 21C2 ways


The total number of ways selecting 2 vowels and 2 consonants


= 5C2 × 21C2



Each of these four letters can be arranged in four ways 4P4



Total numbers of words that can be formed are


24 × 2100 = 50400


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