Question

How many distinct four-letter words can be formed using the word $\text{CENTURY}$.

• A. $840$
• B. $720$
• C. $5040$
• D. $120$

Answer 1

The correct option is A $840$

Word $\text{CENTURY}$ have $7$ letters out of which we have to take $4$ letters and arrange them in order to get all the four lettered words.

We know that the number of ways of arranging "n" things taken "k" at a time, with or without repetition is$nkP=\frac{n!}{(n-k)!}$.

According to the question $n=7$ and $k=4$.

So, number of $4$ lettered words formed are
$74P=\frac{7!}{(7-4)!}=\frac{7!}{3!}\Rightarrow 74P=\frac{7\times 6\times 5\times 4\times 3!}{3!}\Rightarrow 74P=7\times 6\times 5\times 4=840$