How many distinct arrangements are there of PAPA?
I need to count the number of ways to arrange four letters, two of which are P and two of which are A. One way to approach this is to use the formula for permutations of n objects, where some are identical. The formula is n!/(k_1!k_2!...k_m!), where k_1, k_2, ..., k_m are the numbers of identical objects of each type. In this case, n = 4, k_1 = 2 (for P), and k_2 = 2 (for A). So the number of arrangements is 4!/(2!2!) = 24/4 = 6. 