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Maths-

General

Easy

Question

The number of 4 letter words that can be formed using the letters of the word EXPLAIN which begin with a vowel when repetitions are allowed is

1029
207
343
2401

hint Hint:

In the question we know that from the word EXPLAIN we have 3 vowels and to form the new 4 letter word which will start with vowel we will first choose the first letter from the 3 vowels only. Then we know that as the letters can be repeated so the next three letters can be chosen accordingly from all the 7 letters.

The correct answer is: 1029

In the word EXPLAIN, no. of vowels=3 no. of consonants =4
As the 4 letter word has to start with a vowel,
So, the number of ways of choosing the first letter = $blank cubed C subscript 1$ =3
Now for the next three letters we know that any letter from the 7 letters can be used as repetition is allowed.
Therefore, the number of 4 letter words that can be formed using the letters of the word EXPLAIN which begin with a vowel when repetitions are allowed = $3 cross times 7 cross times 7 cross times 7$ =1029

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