Chapter 9, Problem 25CLT

To determine

Calculate the number of distinguishable permutations of the group.

Answer to Problem 25CLT

The number of permutation is $90720$ .

Explanation of Solution

Given: It is given in the question that the alphabets are P, R, I, N, C, I, P, L, E.

Concept Used:

In this, use the concept of distinguishable permutations formula, need to sum up the total number of letters, and count up how much of each letter there are to use in the formula.

Calculation:

Here, the number of letter in P, R, I, N, C, I, P, L, E is $9$ .

So, the permutation is

  $\begin{array}{l}\frac{9!}{2!\cdot 2!}\\ =\frac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{2}\\ =\frac{362880}{4}\\ =90720\end{array}$

Conclusion:

The number of permutation is $90720$ .