### Instruction: Nick, Janet, Huiju, and Amanda go to the World's Largest Brat Fest. Each of them is equally likely to order a meat brat, a hot dog, or a veggie brat. What is the probability that 2 of them order a meat brat, and the other two order hot dogs?### Response: I need to find the number of ways that 2 of them order a meat brat and 2 of them order a hot dog, and divide that by the total number of ways they could order their food.
Since each person has 3 choices, the total number of ways they could order their food is 3^4 = 81.
Now, how many ways could 2 of them order a meat brat and 2 of them order a hot dog?
I could start by choosing which 2 of them order a meat brat.
There are 4 choose 2 = 6 ways to do that.
Then, for each of those ways, the other 2 people must order a hot dog.
There is only 1 way to do that.
So, the number of ways that 2 of them order a meat brat and 2 of them order a hot dog is 6 * 1 = 6.
Therefore, the probability of this event is 6/81, which can be simplified by dividing both numerator and denominator by 3.
The simplified probability is 2/27.