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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    0
    2021-09-06T09:22:10+00:00

    Answer:

    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.

    0
    2021-09-06T09:22:16+00:00

    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

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