Find the number of distinct arrangements of the 8 letters in GIGGLING.Two of the same letter are considered identical (not distinct).

To solve this problem, we use the formula for permutations of multiset: n! / (r1! * r2! * ... * rk!), where n is the total number of items, and r1, r2, ..., rk are the numbers of each type of item.

In the word GIGGLING, there are 8 letters in total.

The letter G appears 3 times, the letter I appears 2 times, and the letters N, L appear 1 time each.

So, we have:

n = 8 (total number of letters) r1 = 3 (number of G's) r2 = 2 (number of I's) r3 = 1 (number of N's) r4 = 1 (number of L's)

Substitute these values into the formula:

Number of arrangements = 8! / (3! * 2! * 1! * 1!)

= 40320 / (6 * 2 * 1 * 1)

= 40320 / 12

= 3360

So, there are 3360 distinct arrangements of the letters in GIGGLING.