counting

[htirwin]

I'm a little confused about some concepts of counting.

How many ways can you select a president, vice president,
and treasurer in a club of 30 people?

Answer: P(30,3) = 24,360

10. You take a group of four people to a Chinese restaurant that has 100 different dishes. All food will be shared among the four of you. How many
ways can you order 4 different dishes?

Answer: C(100,4) = 100*99*98*97 / (4*3*2*1) = 3,921,225

I don't get why in the first question, the answer is not 30 choose 3, whereas in the second problem the answer is 100 choose 4.

[naraku9333]

The first isn't 30 choose 3 because it is a permutation n!/(n-r)! each time one is picked it is no longer a choice.

[htirwin]

So it is because you are making a name for thing that is selected that you must consider it a permutation?

For example, if the second question asked how many ways you can select dishes d1, d2, d3, and d4, from 100 dishes, then you have a permutation because different orderings are different assignments?

[Catfish666]

I think this detail is important: "All food will be shared among the four of you."