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

Mathematics

1 answer:

nikdorinn [45]2 years ago

5 0

Answer:

a. 59049

b. 15120

Step-by-step explanation:

<u>a. If digits can be repeated:</u>

There are 9 possible numbers for each digit

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

<u>b. If digits cannot be repeated.</u>

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

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