Bunuel wrote:
How many different combinations of outcomes can you make by rolling three standard (6-sided) dice if the order of the dice does not matter?
(A) 24
(B) 30
(C) 56
(D) 120
(E) 216
If the order of the dice does not matter then we can have 3 cases:
1. XXX - all dice show alike numbers: 6 outcomes (111, 222, ..., 666);
2. XXY - two dice show alike numbers and third is different: \(6*5=30\), 6 choices for X and 5 choices for Y;
3. XYZ - all three dice show distinct numbers: \(C^3_6=20\), selecting three different numbers from 6;
Total: 6+30+20=56.
Answer: C.
Dear Bunnel
SO basically, when the qs stem says different combination outcomes when order doesnt matter it means that we have to take all possibilities in account:
XXX: i understood: 111, 222, 333, 444, 555, 666
XXY: what about XYX & XXY??? we have not counted this as qs says order doesnt matter?
XYZ: we have just counted 6*5*4/3! as order doesnt matter??
How do you get to know what the qs is asking?
when i read the qs I thought it was asking for all possible outcomes when three dice are thrown. so my answer was 6*6*6 = 216.
what is the difference between order doesnt matter and 216?
Yes, since the order of the dice does not matter then XXY, XYX and YXX are the same for this problem. Similarly, XYZ, XZY, YXZ, ... are also the same.