Question

A 5-digit security code has the numbers 1 through  7 to choose from. If each number can only be used once, how many different combinations are possible?

Answer 1

The first position has 7 options to choose from, the second has 6, the third has 5, and so on. So the number of different arrangements is


`_(7)P_(5)=5!\dbinom75=5!(7!)/(5!(7-5)!)=(7!)/(2!)=2520`