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

To find the number of distinct arrangements of the letters in "SPINNING", we can use the formula for permutations of a multiset. This formula is 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 "SPINNING", there are 8 letters in total, so n = 8.

The letter "S" appears 1 time, so r1 = 1. The letter "P" appears 1 time, so r2 = 1. The letter "I" appears 1 time, so r3 = 1. The letter "N" appears 3 times, so r4 = 3. The letter "G" appears 1 time, so r5 = 1.

Substituting these values into the formula gives us:

8! / (1! * 1! * 1! * 3! * 1!) = 40,320 / (1 * 1 * 1 * 6 * 1) = 6,720.

So, there are 6,720 distinct arrangements of the letters in "SPINNING".