In how many ways can the letters in the word STATISTICS be arranged?
The word STATISTICS has 10 letters. However, there are two S's, three T's, and two I's. Therefore, the number of ways to arrange the letters is:
10!/(2!3!2!)
= 45,360
Therefore, there are 45,360 ways to arrange the letters in the word STATISTICS.
To find the number of ways the letters in the word "STATISTICS" can be arranged, we can use the formula for permutations.
First, we need to determine the total number of letters in the word. In this case, there are 10 letters in total.
However, the letter 'S' appears 3 times, the letter 'T' appears 3 times, and the letter 'I' appears twice. So, we need to account for the repeated letters.
The formula for permutations with repeated elements is given by:
P(n; n1, n2, ..., nk) = n! / (n1! * n2! * ... * nk!)
Where:
n is the total number of elements
n1, n2, ..., nk are the number of times each element is repeated
Using this formula, the number of ways the letters in the word "STATISTICS" can be arranged is:
P(10; 3, 3, 2) = 10! / (3! * 3! * 2!) = 5040 / (6 * 6 * 2) = 84
Therefore, there are 84 ways to arrange the letters in the word "STATISTICS".