Question

A certain model car has a keypad with 5 numbers on the door. To open the door, 5 numbers must be entered in the correct

order and no number can be used more than once. What is the probability that someone could guess the correct code?
OA. Ito
OB.
OC.
OD.

Answer 1

Answer: A.
`(1)/(120)`

Explanation:

Total digits on keypad = 5

According to permutation,

If repetition of digits is not allowed then the number of 5-digits passwords can be formed = 5!

= 5 x 4 x 3 x 2 x 1 [n!=n x (n-1) x (n-2)x ... x 1]

=120

The probability that someone guesses the correct code =
`\frac{\text{Number of correct codes}}{\text{Total possible codes}}`

`=(1)/(120)`

Hence, the correct option is A.