Answer to Question #100695 in Discrete Mathematics for ABDUL SAMED ABDULAI

Question

In how many ways can the word DISCRETE be arranged?

Answer 1

DISCRETE is a 8 letter word, If there were no repeating letters, the answer would have been simply be $8!=40320$

However since there are repeating letters, we need to divide to remove the duplicates accordingly.

There are one D, one I, one S, one C, one R, two E and one T. So only E comes twice.

Therefore, the total number of arrangement of word DISCRETE will be $\frac{8!}{2!}=20160$ .