Question

How many selections of $3$ letters can be made out of letters of word $\text{EMCOT}$?

• A. $20$
• B. $60$
• C. $10$
• D. $30$

Answer 1

The correct option is C $10$

Given word $\text{EMCOT}$ have $5$ letters out of which we have to find number of ways to select $3$ letters.

This can be observed as, first finding out all the possible permutations of $3$ lettered words and then removing the arrangements of those letters.

So, permutation of $5$ letters choosing $3$ letters at a time is ${}^5{P}_3=\frac{5!}{(5-3)!}=60$.

But, we have to remove the arrangements of $3$ letters which is done in $3!=6$ ways.

And this can be done by dividing number of arrangements with number of permutations.

Which means $\frac{60}{6}=10$

So, there will be $10$ different possible combinations or selections of three letters.