Flippys Flowers is designing a special prom corsage that consists of

Varane No order doesn't matter here. Think of this question in this way: There is a lock with a 2-digit and single-letter code (so it goes number, number, letter). The first digit can be any number between 1-4. The second digit can be any number from 5-7. And the last part of the code can be one of the first 5 letters of the alphabet (A, B, C, D or E). Now we want to see how many possible codes one could have on this lock.

The first digit: 4 possible choices.
The second digit: 3 possible choices.
The letter: 5 possible choices.

We cannot change the order of these 3 parts of the code as it is set. We can only select options so it's just: \(4*3*5 = 60\).

Order comes into play when we are asked to arrange things.

Check out: https://gmatclub.com/forum/math-combina ... 87345.html
and: https://gmatclub.com/forum/permutations ... 50835.html

It's actually the opposite: you'd multiply by 3! if order matters. If you think of the question "how many sets of three different letters can you pick from the letters A, B and C?" then order does not matter, because we're just picking a set, and the answer is one, because we have to pick all three of the letters. But if you're asked "how many different three-letter sequences can you make using all three of the letters A, B and C?" then we're putting the letters in order, and now we want to count all 3! = 6 of the different orders we can put the letters in (ABC, ACB, BAC, BCA, CAB, CBA). So if the order of three things matters, the answer will be 3! times as big as when the order does not matter.

As for the corsage question in this thread, there's no way to answer it. We have 5*3*4 = 60 choices of flower. But we don't know how we're arranging the flowers to make the corsage "design" the question asks about. If the flowers are in a row, then their order would matter, and the answer would be 3!*60 = 360. If, as I think is typical of a corsage (I'm no expert), the flowers are in a kind of triangle or circular arrangement, then we'd have 2! circular permutations of the flowers, and the answer would be 2!*60 = 120. If the flowers somehow aren't being arranged at all, which doesn't make much sense, then the answer is 60 -- I'd bet that's the OA, but the question isn't well-conceived.