Question

Mike forgot the last three digits of his friend's telephone number. He only remembers that the digits are not the same. What is the probability he dials the correct telephone number on the first try

Answer 1

1/720 = 0.0014 = 0.14% probability he dials the correct telephone number on the first try.

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order of the digits is important, which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

Desired outcomes:

One correct number, so
`D = 1`

Total outcomes:

3 non-repeated digits, so permutations of 3 digits from a set of 10(all digits). So

`T = P_(10,3) = (10!)/(7!) = 10*9*8 = 720`

What is the probability he dials the correct telephone number on the first try?

`p = (D)/(T) = (1)/(720) = 0.0014`

1/720 = 0.0014 = 0.14% probability he dials the correct telephone number on the first try.