# Question 6: 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: 2 different vowels and 2 different consonants are to be selected from the English alphabet. Since there are 5 vowels in the English alphabet, number of ways of selecting 2 different vowels from the alphabet = Since there are 21 consonants in the English alphabet, number of ways of selecting 2 different consonants from the alphabet Therefore, number of combinations of 2 different vowels and 2 different consonants = 10 × 210 = 2100 Each of these 2100 combinations has 4 letters, which can be arranged among themselves in 4! ways. Therefore, required number of words = 2100 × 4! = 50400

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