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  4. Out of seven consonants and four vowels, the number of words of six letters, formed by taking four consonants and two vowels is (Assume that each ordered group of letter is a word) -

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Q. Out of seven consonants and four vowels, the number of words of six letters, formed by taking four consonants and two vowels is (Assume that each ordered group of letter is a word) -

Permutations and Combinations

Solution:

Number of selections of $4$ consonants out of $7$ is ${ }^7 C _4$
Number of selections of 2 vowels from $4$ is ${ }^4 C_2$
Arrangement of words in $6 ! $ ways
Desired words : ${ }^7 C _4 \,\,\, { }^4 C _2\,\,\, 6 !=151200$