Chapter 12.7, Problem 22STP

To determine

To find the number of ways the letters in the word STATISTICS be arranged.

Answer to Problem 22STP

F) $50,400$

Explanation of Solution

Given information:

The given options are:

F) $50,400$

G) $20,800$

H) $15,400$

J) $3480$

The number of ways the letters in the word STATISTICS can be arranged is found using the formula below:

  $\begin{array}{l}\frac{\text{n!}}{\text{n1!n2!}\mathrm{..}\text{nk!}}\\ =\frac{10!}{3!3!1!2!1!}\left[\begin{array}{l}\text{S=n1, T=n2, A=n3, I=n4, C=n5}\\ \text{n}1=3,\text{ n2=3, n3=1, n4=2, n5=1}\end{array}\right]\\ =\frac{3628800}{72}\\ =50400\end{array}$

Hence, the word STATISTICS can be arranged in $50400$ ways.