Answer to Question #322478 in Combinatorics | Number Theory for Jesrene31

Question

Determine the number of distinguishable permutations of the letters ELEMENT. *

A.140

B.340

C.640

D.840

Answer 1

Different letters in word ELEMENT:

E,L,M,N,T - 5

Number of equal letters - 3

All letters -7

$P_7=7!$

The number of distinguishable permutations of the letters is $\frac{7!}{3!}=840$

Answer : D. 840