A classic counting problem is to determine the number of different ways that the letters of "generally""generally" can be arranged. Find that number.

Final answer:

To determine the number of arrangements for the word 'generally', one calculates 9 factorial divided by the factorial of the counts of each repeated letter. With 'E' and 'L' repeating twice each, the calculation is 9! / (2! × 2!) resulting in 90720 unique arrangements.

Explanation:

Calculating Arrangements of the Word 'GENERALLY'

To calculate the number of different ways the letters in the word 'generally' can be arranged, we have to take into account the repeated letters. The word 'generally' has 9 letters with the following repetitions: G-1, E-2, N-1, R-1, A-1, L-2, and Y-1. The formula to calculate the permutations of a set of objects where there are duplicates is the factorial of the number of objects divided by the product of the factorials of the number of duplicates for each object.

Thus, to find the number of arrangements, we would calculate 9! (9 factorial) and then divide it by the product of the factorials of the repeated letters, which are E and L. This gives us 9! / (2! × 2!), or 362880 / (2 × 2), which simplifies to 90720 unique arrangements for the letters in 'generally'.

This combinatorial approach is a useful exercise in understanding how to count arrangements and can be applied more broadly to comprehend more intricate probability and statistics problems

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