6. In the Pirates of the Aegean video game, you may have to investigate 0, 1, 2, 3, 4, or 5 grottoes without success before you finally locate a treasure chest. You conclude that the probability you will have to investigate at mostxgrottoes without success is , and F(5) = 1. (Remember that is the number of permutations(ordered lists withoutreplacement) of kitems from npossibilities.)a) What is the probability you will have to investigate exactly 3 grottoes without success?b) What is the expected numberE(X) of grottoes you will investigate without success?c) What is the variance Var(X) of the number of grottoes you will investigate without success?