Find the number of 7 letters words that contain at least one vowel.

Expert Solution

We have to find the number of 7 letter words that contains at least one vowel.

Now, each of 7 places in the word can contain any of the 26 letters in the alphabet.

So, the number of all possible cases is 26*26*...*26(7 times).

Now, in stead of finding out the number of words that contain at least one vowel, we find out the complement, ie. the number of words that contain no vowel.

Now, there are 5 vowels- a,e,i,o,u.

So, except 5 vowels, there are 26-5, ie. 21 consonants.

Now, this means that each of the 7 places in the word, have 21 options to choose from.

So, the number of favourable cases for no vowels is 21*21*...*21(7 times).

Now, we note that

Number of 7 letter words that contains at least one vowel

=Total number of 7 letter words-Number of 7 letter words that contains no vowels

So, the answer is 6230721635.

orchestra answered 1 year ago

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