Question

How many five-digit numbers can you make from rolling a standard die to create the digits if the digits can be repeated?

A) 6,250
B) 7,776
C) 15,625
D) 20,000

Answer 1

To find the number of five-digit numbers that can be made by rolling a standard die five times with repetition allowed, calculate 6 to the power of 5, resulting in 7,776 possibilities. The correct answer is B) 7,776.

Step-by-step explanation:

The question asks how many different five-digit numbers can be created by rolling a standard six-sided die five times, where the digits can be repeated. This is a problem of permutations with repetition. Since each die roll is an independent event, and each roll has 6 possible outcomes, the number of five-digit numbers created by rolling a die five times is 6 to the power of 5, which is 7,776 possible numbers.

To calculate this, you would multiply the number of possibilities for each digit. Since there are 6 possibilities for the first digit, 6 for the second, and so on, the calculation is:

• 6 (possibilities for 1st digit) x 6 (for 2nd) x 6 (for 3rd) x 6 (for 4th) x 6 (for 5th) = 7,776.

Thus, the correct answer to the student's question is B) 7,776.