<p>It's not an SAT question, but it's hard though.
There are three kinds of food, and you want to choose 5 dishes from the three kinds of food, so how many choices you have? ( you can choose 5 dishes from one kind of food if you want)</p>
<p>This is just 3^5 = 243. </p>
<p>For each dish there are 3 choices. You’re selecting each dish independently of the others. By the counting principle you multiply 3<em>3</em>3<em>3</em>3 = 3^5 = 243.</p>
<p>3^5 counts the order of the dishes as separate cases. The question does not make it clear.</p>
<p>If ABCAB is different than AABBC, then 3^5 is the answer. But if the order does not matter, it’s a harder question…</p>
<p>Actually it’s not. If ABCAB is not different than AABBC, then it’s way easier: just list them out!</p>
<p>0A, 0B, 5C.
0A, 1B, 4C
0A, …
B runs from 0 to 5.
1A, 0B, 4C.
1A, 1B, 3C.
1A, 2B, 2C.
1A, 3B, 1C.
1A, 4B, 0C.</p>
<p>B runs from 0 to 4.
2A, 0B, 3C
2A, 1B, 2C.
2A, 2B, 1C.
…</p>
<p>Contine doing so!</p>
<p>Then you have the sum =6(since B runs from 0 to 5) 5+ 4 + 3 +2 +1= 21</p>
<p>Source: my 16 year old brain.</p>