Chapter 13.2, Problem 6CFU

To determine

To find: The number of ways in which the 2 red light, 4 yellow lights, 5 blue lights, 1 green light and 2 pink lights that can be arranged on the string of the lights.

Answer to Problem 6CFU

The number of combination is $7567560$ .

Explanation of Solution

Consider that the letter CLASSICAL has 9 letters with 2 A, 2 C, 2 Sand two L.

Consider that the number of different permutation of $n$ things in which the $p$ is the one kind and $q$ is the another kind taken at all the time is,

  $\frac{n!}{p!q!}$

Then, for the given data.

  $\begin{array}{c}\frac{n!}{p!q!}=\frac{14!}{2!\cdot 4!\cdot 5!\cdot 2!}\\ =7567560\end{array}$