Question

In how many different, distinguishable orders can the letters of the word mathematics be arranged?
A)39,916,800
B)4,989,600
C)6,652,800

Answer 1

Answer:

B)4,989,600

Step-by-step explanation:

The letters of 'MATHEMATICS'  contains 11 letters.

The following letters repeats twice, TT,MM,AA.

When we talk of distinguishable wasy, we are referring to arrangement without repetition.

Therefore the letters of "MATHEMATICS" can be arranged in $\frac{11!}{2!2!2!}=4,989,600$ distinguishable ways.

The correct answer is B.