Final answer:
To calculate the number of 5-digit combinations on a keypad with 6 keys, one must raise 6 to the power of 5, resulting in 7776 different combinations.
Step-by-step explanation:
The student has asked to calculate the total number of possible 5-digit combinations on a keypad with only 6 keys. To find this, we use the principle that the number of possible outcomes (or microstates) of any repeated independent situation is the base number of choices raised to the power of the number of times you are making those choices. Since there are 6 keys and each key can be used in each of the 5 positions, the total number of combinations is 6 to the power of 5, which is 6 x 6 x 6 x 6 x 6.
To calculate this, we do the math: 6 multiplied by 6 is 36, 36 multiplied by 6 is 216, 216 multiplied by 6 is 1296, and finally, 1296 multiplied by 6 gives us 7776. Therefore, there are 7776 possible 5-digit combinations on a keypad with 6 keys.