Question

How many words can be formed by taking four different letters of the word $MATHEMATICS$ ?

• A. $756$
• B. $1680$
• C. $2454$
• D. $18$

Answer 1

The correct option is C $2454$

The word MATHEMATICS has $2M^{\prime }s,2T^{\prime }s,2A^{\prime }s$ and $1$ each of $H,E,I,CandS$.

Thus 4 letters can be chosen in 3 ways.

1. 2 alike of one kind and 2 alike of second kind.

Number of words $={{}^{3}C}_2\times \frac{4!}{2!2!}=18$

2. 2 alike of one kind and 2 different.

Number of words $={{}^{3}C}_2\times {{}^{7}C}_2\times \frac{4!}{2!}=756$

3. All different letters.

Number of words $={{}^{8}C}_4\times 4!=1680$

So total number of words $=2454$