Question

How many different words can be formed out of the letters of the word "MORADABAD" taken $4$ at a time

• A. 620
• B. 622
• C. 626
• D. 624

Answer 1

The correct option is C 626

The word MORADABAD has $2$ D's,3 A's,and one M,O,R and B each.
No. of words with $4$ diff. alphabets $=$ $\left(\begin{array}{c}6\\ 4\end{array}\right)\times 4!$
No. of words with 2alike,2diff. alphabets $=$ $\left(\begin{array}{c}5\\ 2\end{array}\right)\left(\begin{array}{c}2\\ 1\end{array}\right)\frac{4!}{2!}$
No. of words with $2$ alike, $2$ other alike alphabets $=$ $\left(\begin{array}{c}2\\ 2\end{array}\right)\frac{4!}{2!2!}$
No. of words with $3$ alike and $1$ diff. alphabet $=$ $\left(\begin{array}{c}5\\ 1\end{array}\right)\times \frac{4!}{3!}$
Hence, the total number of words $=626$.