Question:
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 ?
Answer:
Number of vowels = 5
Number of consonants = 21
Now we have to form words with 2 different vowels and 2 different consonants.
Number of words = 5C2 * 21C2 * 4! (4! is because we can arrange the letters in 4! ways)
= (5*4)/2 * (21*20)/2 * 24 (4! = 24)
= 20/2 * 420/2 * 24
= 10*210*24
= 50400
So total number of words = 50400
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