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

Solutions

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

Next > < Previous

Related Solutions

Find the number of five letter words that can be formed from the letters of the...

Find the number of five letter words that can be formed from the letters of the word PROBLEMS. ( please explain with details.) (a) How many of them contain only consonants? (b) How many of them begin and end in a consonant? (c) How many of them begin with a vowel? (d) How many contain the letter S? (e) How many begin with B and also contain S? (f) How many begin with B and end in a vowel? (g)...

Consider arrangements of the letters NEWBIT. How many arrangements start or end with a vowel?

A person has to create a code. The code must contain exactly 7 letters. The first...

A person has to create a code. The code must contain exactly 7 letters. The first letter must either a N, P, R, or T. The second letter must be a vowel that is not I, O, or U. The third letter must be a consonant that is not a D, F, H, or J. The fourth letter must be a vowel that is not an O or U. The fifth letter must be a consonant that is not a...

Let S = {1,2,3,...,10}. a. Find the number of subsets of S that contain the number...

Let S = {1,2,3,...,10}. a. Find the number of subsets of S that contain the number 5. b. Find the number of subsets of S that contain neither 5 nor 6. c. Find the number of subsets of S that contain both 5 and 6. d. Find the number of subsets of S that contain no odd numbers. e. Find the number of subsets of S that contain exactly three elements. f. Find the number of subsets of S that...

1) Find the number of unique ways that the letters in the word can be arranged:...

1) Find the number of unique ways that the letters in the word can be arranged: KERFUFFLE 2) A survey of commuters found that 313 owned a motorcycle, 232 owned a car, 269 owned a moped, 98 owned a car and a moped, 57 owned only a car, 104 owned a motorcycle and moped but not a car, 69 owned all three, and 64 owned none. What proportion of people surveyed owned only a moped? Leave your answer as an...

A password is a sequence of letters (a–z) and digits (0–9). Find the number of passwords...

A password is a sequence of letters (a–z) and digits (0–9). Find the number of passwords of length 10 under the constraints in (a), (b) or (c) (three separate problems). Express your answer using factorials and integers, products and ratios of them, and/or sums of such things. (a) There are 3 letters and 7 digits, and at most one ‘9’. (b) There are 6 letters and 4 digits, and no digit occurs twice. (c) No letters are used BUT the...

find a recurrence relation for the number of bit strings of length n that contain the...

find a recurrence relation for the number of bit strings of length n that contain the string 10. What are the initial conditions? How many bit strings of length eight contain the string 10

find a recurrence relation for the number of bit strings of length n that contain two...

find a recurrence relation for the number of bit strings of length n that contain two consecutive 1s. What are the initial conditions? How many bit strings of length eight contain two consecutive 1s

1. How many permutations of the 26 letters are there that contain none of the sequences...

1. How many permutations of the 26 letters are there that contain none of the sequences ROCK, STONE, PLUG, FIT or HAY?

Problem 1 - Find the Diphthongs A diphthong is a composite vowel sound composed of two...

Problem 1 - Find the Diphthongs A diphthong is a composite vowel sound composed of two simple vowel sounds. We're going to be looking for these in words. For instance "ay" is normally a diphthong for instance in the words "lay" and "day", as is "ou" for instance in "loud," "lout." We're going to simplify this by looking only for two vowels in a row in a word regardless of whether they are sounded out as diphthongs or not. Let...

Subjects