How many distinct arrangements can be made from the letters of the word “MAHIRAP”?

To solve this problem, we need to 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.

Step 1: Count the total number of letters in the word "MAHIRAP". There are 7 letters.

Step 2: Count the number of each type of letter. There are 2 As, 1 M, 1 H, 1 I, 1 R, and 1 P.

Step 3: Substitute these values into the formula. The number of distinct arrangements is 7! / (2! * 1! * 1! * 1! * 1! * 1!) = 5040 / 2 = 2520.

So, there are 2520 distinct arrangements that can be made from the letters of the word "MAHIRAP".