Answer to Question #259738 in Discrete Mathematics for rtf

Question

How many number of strings that can be formed by ordering the letters given:

(a) SCHOOL

(b) CLASSICS 

Answer 1

Let us use the formula for permutations with repetitions.

(a) The number of strings that can be formed by ordering the letters of the string SCHOOL is equal to

$P_6(2,1,1,1)=\frac{6!}{2!1!1!1!}=\frac{720}2=360.$

(b) The number of strings that can be formed by ordering the letters of the string CLASSICS is equal to

$P_8(3,2,1,1,1)=\frac{8!}{3!2!1!1!1!}=\frac{40320}{12}=3360.$