A string has the form 0???0, where each ? could be a 0 or a 1. How many possible strings are there?

lockers to members of a baseball team. Assume that you are assigning one of 15 available lockers to each of the 5 players on the team. In how many ways can this assignment be made so that each player gets a different locker?

5 different elves (Sue, Marcia, Cher, Jane, and Johnny) each make a different toy (ball, car, top, sled, or train). Each elf wears a different color (green, yellow, blue, red, or orange) and each builds a different number of toys. Use the poem below to decipher which elf wore what color and made how many of what toy!! ---------------------------------------------------- The Boss's pack held thirty toys Made by his elfin crew; And though none made the same amount, Each elf made more than two. The elf named Cher made one more toy Than the elf who dressed in reds, But Cher made one less holiday toy Than the elf who made the sleds. Spry Johnny elf made racing cars; Five toys were made by Jane. The elf who dressed in yellow suits Made each and every train. The elf who always dressed in green Made one-third as many as Sue. Cute Marcia elf was dressed in orange, And one elf dressed in blue. The elf who made the spinning tops Made the most toys of them all. Another perky, smiling elf Made each…