Question

Outside a​ home, there is aa 5-key keypad with letters Upper A comma Upper B comma Upper C comma Upper D and comma Upper EA, B, C, D and, E that can be used to open the garage if the correct fivefive​-letter code is entered. Each key may be used only once. How many codes are​ possible?

Answer 1

Total letters in the keypad = 5

Number of ways to use first code = 5 (i.e any of the five letters)

Number of ways to use second code = 4 (i.e any of the letters except the letter used in first code)

Number of ways to use third code = 3 (i.e any of the letters except the letter used in first and second code)

Number of ways to use fourth code = 2 (i.e any of the letters except the letter used in first, second and third code)

Number of ways to use fifth code = 1 (i.e any of the letters except the letter used in first, second, third and fourth code)

Total number of codes possible = 5 * 4 * 3 * 2 * 1 = 120 (ans)