Certainly! Let's go through this problem step by step.
### Understanding the Problem
Brittan and Carlita each bought one raffle ticket at a fundraising benefit where 100 tickets were randomly sold. The question asks us to calculate the probability that Brittan got ticket number 7 and Carlita got ticket number 32.
### Step-by-Step Solution
Step 1: Identify whether to use permutation or combination
- In this problem, the order of ticket numbers matters (i.e., Brittan has a specific ticket number 7 and Carlita a specific ticket number 32). Since we are dealing with specific positions (specific tickets for specific people), we consider permutations.
Step 2: Determine the probability for each event independently
- Probability of Brittan getting ticket number 7:
There is only 1 specific ticket number 7 among 100 tickets.
[tex]\[
P(\text{Brittan gets ticket 7}) = \frac{1}{100}
\][/tex]
- Probability of Carlita getting ticket number 32:
Similarly, there is only 1 specific ticket number 32 among 100 tickets.
[tex]\[
P(\text{Carlita gets ticket 32}) = \frac{1}{100}
\][/tex]
Step 3: Combine the probabilities of independent events
- Since the events (Brittan getting ticket 7 and Carlita getting ticket 32) are independent, we multiply their probabilities to get the combined probability.
Combined Probability:
[tex]\[
P(\text{Both Brittan and Carlita get their specific tickets}) = P(\text{Brittan gets ticket 7}) \times P(\text{Carlita gets ticket 32}) = \frac{1}{100} \times \frac{1}{100} = \frac{1}{10000} = 0.0001
\][/tex]
### Conclusion
The probability that Brittan got ticket number 7 and Carlita got ticket number 32 is [tex]\(0.0001\)[/tex] or [tex]\( \frac{1}{10000} \)[/tex].
