Question

A 5-digit combination lock with digits 0-9 can be opened only if a correct combination of digits is chosen. Find the probability of guessing the correct combination if: A. no digit is repeated a0 a1 B. digits can repeat and zero is not one of the digits in the combination a2 a3

Answer 1

A. 0.3204

B. 0.59049

Explanation:

Data:

The total number of combinations:

=
`(10)^(5) = 100 000`

A.

The number of ways =
`10 * 9 * 8* 7 = 30 240`

The probability for an event P taking place =
`(30 240)/(100 000) \\= 0.3 024`

B.

Number of ways to arrange the subjects =
`(9)^(4) = 59 049`

The probability =
`(59 049)/(100 000) \\= 0.59049`

Answer 2

The total number of combinations without restrictions is

10 * 10 * 10 * 10 * 10 = 100000

Problem A

10 * 9 * 8 * 7 * 6 = 30240

the number of ways the combination can be set up with no repetition.

The probability of such an event is P = 30240 / 100000 = 0.3024

Problem B

The number of ways that can be done with repetition and no zeros is

9 * 9 * 9 * 9 * 9 = 59049

The probability of such an event is

P = 59049 / 100000 = 0.59049