# Top Score Probability Question...wrong?

#### djeffreyt

##### Senior Member
10+ Year Member
7+ Year Member
So on the Topscore test 2, QR, question 15 is:

A florist purchased 3 yellow, 2 pink, and 5 red roses. How many 3 rose arrangements are possible?

a) 10/3
b) 120
c) 30
d) 10
e) 110

The answer according to the solutions is (b)

The reasoning on Topscore is:
Selecting any 3 of the 10 roses;
Using the conbinations formula nCr where a combinations of n things taken r at a time, and is written as n! / [r!(n-r)!]; this yields 10*9*8/3! = 120;

This confuses me. Are we supposed to ignore the fact that the roses are grouped by color? The formula they give works if we consider each rose as completely unique from the other 9. But if we consider that roses as part of color groups, the number of possible combinations is way way smaller. I don't know if my confusion makes sense...for example

Let's say
combo a is red rose 1, red rose 2, and pink rose 1
combo b is red rose 1, red rose 3, and pink rose 1
combo c is red rose 1, red rose 2 and pink rose 2

if we consider each of the roses as completely individual, then all three of these combos are completely unique and there are 120 combos.

but if we consider that red rose 1,2,3,4, and 5 are all just "red roses" and so forth for the other colors, all these combinations are the same, and would only count once, and the total # of combos is way less.

Did Topscore mess up, or did the question give excess information about the rose colors that threw me off or am I just completely wrong?