Question

8. A home security system has a pad with 9 digits (1 to 9). Find the number of possible 5-digit pass codes:

Answer 1

Answer:

a. 59049

b. 15120

Step-by-step explanation:

a. If digits can be repeated:

• There are 9 possible numbers for each digit

That is:  possible 5-digit pass codes are 9×9×9×9×9=$9^{5}$=59049

b. If digits cannot be repeated.

There is

• 9 possibility for the first digit,

• 8 possibility for the second digit

• 7 possibility for the third digit

• 6 possibility for the fourth digit

• 5 possibility for the fifth digit

That is:  possible 5-digit pass codes are 9×8×7×6×5=15120