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Lelu [443]
3 years ago
12

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]3 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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