To determine the probability that Jaxon will enter the correct passcode, we need to follow these steps:
1. Identify the Total Number of Possible Permutations:
Jaxon remembers that the passcode contains the digits 1, 2, 3, and 4. Therefore, we need to find the total number of different ways to arrange these four digits.
The total number of unique arrangements (permutations) of four distinct digits can be found using the factorial function. For 4 digits, the number of permutations is [tex]\( 4! \)[/tex] (4 factorial).
[tex]\[
4! = 4 \times 3 \times 2 \times 1 = 24
\][/tex]
So, there are 24 different ways to arrange these four digits.
2. Determine the Number of Correct Permutations:
Since there is only one specific correct passcode, the number of correct permutations is 1.
3. Calculate the Probability:
The probability of Jaxon entering the correct code is the ratio of the number of correct permutations to the total number of permutations.
[tex]\[
\text{Probability} = \frac{\text{Number of correct permutations}}{\text{Total number of permutations}}
\][/tex]
Substituting the values we found:
[tex]\[
\text{Probability} = \frac{1}{24}
\][/tex]
4. Convert the Probability to a Readable Format:
This fraction can also be expressed as approximately [tex]\( 0.0417 \)[/tex] as a decimal (0.041666... to be more precise).
Now, let's match this probability with the provided options:
- A. 1 in 4
- B. 1 in 16
- C. 1 in 24
- D. 1 in 32
Clearly, the correct option is:
C 1 in 24
