Respuesta :
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=[tex]9^{5}[/tex]=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
The Number of possible 5-digit passcodes If digits can be repeated is 59,049 and If digits can not be repeated is 15,120.
What is Combination?
The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
[tex]^nC_r = \dfrac{n!}{r!(n-r)!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
We know that the number of choices when the digits can be repeated is 9, therefore, each of the 5 places has 9 possibilities. Thus, the number of possible 5-digit passcodes If digits can be repeated,
Number of possible 5-digit passcodes = ⁹C₁ x ⁹C₁ x ⁹C₁ x ⁹C₁ x ⁹C₁
= 59,049
Now, as the number can not be repeated, therefore, once a number is been chosen, it can not be repeated, therefore, the possibilities of the number will be reducing,
Number of possible 5-digit passcodes = ⁹C₁ x ⁸C₁ x ⁷C₁ x ⁶C₁ x ⁵C₁
= 15,120
Hence, the Number of possible 5-digit passcodes If digits can be repeated is 59,049 and If digits can not be repeated is 15,120.
Learn more about Combination:
https://brainly.com/question/11732255
