Problem

How many different ways can the letters of "statistics" be arranged? The number of different ways that the letters of "statistics" can be arranged is (Simplify your answer.)

Solution

Step 1 :The word 'statistics' has 10 letters in total. Among these, the letter 's' appears 3 times, the letter 't' appears 3 times, the letter 'i' appears 2 times, and the letters 'a' and 'c' appear once each.

Step 2 :The number of different ways to arrange n items, where some items are identical, is given by the formula \(\frac{n!}{r1! * r2! * ... * rk!}\), where n is the total number of items, and r1, r2, ..., rk are the numbers of each type of identical item.

Step 3 :In this case, n = 10, r1 = 3 (for 's'), r2 = 3 (for 't'), r3 = 2 (for 'i'), r4 = 1 (for 'a'), and r5 = 1 (for 'c').

Step 4 :Substituting these values into the formula, we get \(\frac{10!}{3! * 3! * 2! * 1! * 1!} = 50400\).

Step 5 :Final Answer: The number of different ways that the letters of 'statistics' can be arranged is \(\boxed{50400}\).

From Solvely APP
Source: https://solvelyapp.com/problems/7254/

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