Final answer:
The number of different 'words' that can be composed by shuffling the letters of 'statistics' is 100,800. The calculation involves using the factorial formula adjusted for the repeated letters 's' and 'i'. The permutations are 10 factorial divided by the factorial of each of the repeated letters.
Step-by-step explanation:
The question asks for the number of different 'words' formed by shuffling the letters of the word 'statistics'. Calculating the permutations of the letters in 'statistics' requires accounting for the repetitions of certain letters. The word contains one 't', three 's', three 'i', and one 'a' letters. When there are repeated letters, the formula to calculate the permutations is:
n! / (n1! * n2! * n3! * ...)
Where n is the total number of letters, and n1, n2, n3, etc., represent the factorial of the count of each repeated letter. For 'statistics', the calculation is:
10! / (3! * 3! * 1! * 1!)
The factorial of 10 (10!) is the total number of permutations without the repetition of letters, which equals 3,628,800. The factorial of 3 (3!) for the letter 's' and the letter 'i' indicates the number of ways to arrange each set of three identical letters, which equals 6 (3*2*1). Accounting for both sets of 's' and 'i' letters, we get:
3,628,800 / (6 * 6) = 3,628,800 / 36 = 100,800
The correct number of different 'words' that can be composed from the letters of 'statistics' is 100,800, which is not one of the provided options.