## 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

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.

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Sample response: No, Jillian is not correct. According to the fundamental counting principle, the total number of possible codes would be (40)(40)(40) = 64,000. Jillian multiplied by 3 instead of multiplying the number of possibilities for each digit.

Step-by-step explanation:

Sample response: No, Jillian is not correct. According to the fundamental counting principle, the total number of possible codes would be (40)(40)(40) = 64,000. Jillian multiplied by 3 instead of multiplying the number of possibilities for each digit.

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 to Thus, out of total set of numbers (i.e ), the numbers can be repeated.

This means for all three code numbers the opportunity of choosing a number is same  i.e. between Now, the first digit of the code can be any number between Like wise the second and third  digit of the code can be any number between Thus. the possible number of codes with repetition allowed are Hence, Jillian is not correct

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