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The English alphabet has 5 vowels and 21 consonants. How many words with 2 different vowels and 2 different consonants can be formed from the alphabet? |
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Answer» No. of ways of selecting 2 vowels out of 5 vowels `= .^(5)C_(2)`. No. of ways of selecting 2 consonants out of 21 consonants `= .^(21)C_(2)`. No. of ways to arrange 2 vowels and 2 consonants i.e., 4 letters = 4! Therefore total no. of words `= .^(5)C_(2) xx .^(21)C_(2) xx 4!` `= (5 xx 4)/(2 xx 1) xx (21 xx 20)/(2 xx 1) xx 24` `= 10 xx 210 xx 24` `= 50400` |
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