How many Five letter word using letters a a g m m r?

To find the number of five-letter Words that can be formed using the letters a, a, g, m, and m, we can use the formula for permutations of multiset. The total permutations of the letters is given by ( \frac{5!}{2! \times 2!} = \frac{120}{4} = 30 ). Therefore, there are 30 distinct five-letter arrangements that can be formed with the given letters.