Question

How many words can be made from the letters of the word MONDAY assuming that no letter is repeated if 4 letters are used at a time?

Answer 1

Make blank space of $4$ section and mention 1st, 2nd, 3rd, and 4th position in it and do fix either of the letters and then go to the next position and so on and try to make arrangements of the specified positions.

Complete step by step answer:
Given: A word ‘MONDAY’ is given in which $6$letters of the alphabet are used. Out of these $6$ letters we have to find the total number of words which can be formed by $4$ letters.
As there are $6$ letters in the word ‘MONDAY’. These $6$ letters are M, O, N, D, A, Y.
Words of $4$letters are to be formed.
We will draw a box here of four sections. Each of the section has mentioned by position
1st_, _2nd, __3rd, _4th
As the repetitions are not allowed.
So, total numbers of possibilities by which 1st position can be filled are $6$.
Now, we have $5$ letters available.
So, total numbers of possibilities by which 2nd position can be filled are $5$.
Now, we have $4$ letters available.
So, the total number of possibilities by which the 3rd position can be filled are $4$.
Now, we have $3$ letters and only one position is left.
So, the total number of possibilities by which the 4th position can be filled are $3$.
The total number of $4$ letters word can be formed by the $6$ letters of the word MONDAY

$=$Total no. of possibilities by which 1st position can be filled$\times$total no. of possibilities by which 2nd position can be filled$\times$ total no. of possibilities by which 3rd position can be filled$\times$ total no. of possibilities by which 4th position can be filled.

= 6 \times 5 \times 4 \times 3 \\\ = 360 \\\ \end{gathered} $$ _Hence, 360 words can be formed._ **Note:** First find all the possibilities of the specific position and then multiply all of the possibilities of the positions to get the required answer. Alternatively, we can find the number of words can be made from the letters of the word MONDAY assuming that no letter is repeated if $$4$$letters are used at a time, using formula of permutation as ${}^6{P_4} = \dfrac{{6!}}{{(6 - 4)!}} = \dfrac{{6!}}{{2!}}.$