Question

A combination lock has a code consisting of 3 numbers, each of which can be 0 to 39, with numbers repeated. Jillian says that there are only 120 possible codes. Is Jillian correct? If not, explain her error.

Answer 1

Answer:

Jillian is not correct

Jillian has summed up the possible number of codes for each digit instead of multiplying it

Step-by-step explanation:

The lock has a code that consists of 3 number

It is given that the number in the lock code can be used between $0$ to $39$

Thus, out of total $40$ set of numbers (i.e $0-39$), the numbers can be repeated.

This means for all three code numbers the opportunity of choosing a number is same  i.e. between  $0-39$

Now, the first digit of the code can be any number between  $0-39$

Like wise the second and third  digit of the code can be any number between  $0-39$

Thus. the possible number of codes with repetition allowed are

$40 * 40* 40\\64000$

Hence, Jillian is not correct

Jillian has summed up the possible number of codes for each digit instead of multiplying it

Answer 2

39*3=117 not 120 so that is why she is wrong