Question

How many words can be made from the letters of the word MONDAY assuming that no letter is repeated if all letters are used but first is a vowel?

Answer 1

Hint: As given in the question no letter is repeated so if we have a letter of first place from 6 letters then for second place we will have 5 letters to choose and so on. We can multiply all numbers together to get the total possible number of words.

Complete step-by-step answer:
Given word is ‘MONDAY’
Total number of letter is 6
Number of vowels is 2.
So we can choose a letter in the first place from right side from 2 ways.
Then we can choose the number at second place from the remaining 5 letters. So we can choose letters in second place from 5 ways. As there is no repetition we can choose a letter at third place from 4 ways . Similarly letter at fourth place can be chosen from 3 ways , letter at fifth place can be chosen from 2 ways , and letter at sixth place can choose in 1 way.
So total possible number of words is $ 2\times 5\times 4\times 3\times 2\times 1=240 $

Note: As there is no repetition allowed so we need to remember which letter we used , will not count to fill the next place.
That’s why we decreased the number by 1 for each place.
First place can be filled by vowels only, that is why we need to remember we only need to count the total number of vowels to choose a letter in the first place.