360360. We need 15P5, permutations of 15 items taken 5 at a time. We're arranging 5 items out of 15, where order matters, so we use permutations. nPr = n! / (n-r)!, so 15P5 = 15! / 10!. This is the product of 5 numbers counting down from 15: 15 x 14 x 13 x 12 x 11 = 360360. So 15P5 = 360360.