probability problem?

Question

A bowl of sweets contain 2 fruit gums , 3 mints and five toffees. three sweets are to be chosen at random and without replacment from the bowl .
construct a propability three to show all possiblties

Answer 1

Denote fruit gum by F, mint by M and toffee by T.
The set of all possible outcomes is {FFM, FFT, FMF, FMM, FMT, FTF, FTM, FTT, MFF, MFM, MFT, MMF, MMM, MMT, MTF, MTM, MTT, TFF, TFM, TFT, TMF, TMM, TTT,}

For each outcome you can calculate the probability as follows:
FFM=2/10x1/9x3/8 = 6/720 = 0.008
FFT=2/10x1/9x5/8 = 10/720 = 0.013
FMF=2/10x3/9x1/8 = 6/720 = 0.008
and so on. This list, if I'm correct, comprises all the possible outcomes and they are mutually exclusive, so if you add all the probabilities they sould total 1.

If you wish to know, for example, the probability of getting two mints, then just add together all the relevant probabilities
FMM = 0.016
MFM = 0.025
MMF = 0.016
MMT = 0.041
MTM = 0.041
TMM = 0.041
Prob = 0.18

Answer 2

first sweet second sweet third sweet
mint (3/10)........................mint (2/9) ...............................mint (1/8)
.............................................................................................toffee (5/8)
............................................................................................. fruit (2/8)
........................................... toffee (5/9................................mint (2/8)
.............................................................................................. toffee (4/8)
.............................................................................................. fruit (2/8)
................................................ fruit (2/9) ................................ mint (2/8)
..................................................................................................toffee (5/8)
................................................................................................... fruit (1/8)

toffee (5/10) mint (3/9) mint (2/8)
toffee (4/8)
fruit (2/8)
toffee (4/9) mint (3/8)
toffee (3/8)
fruit (2/8)
fruit (2/9) mint (3/8)
toffee (4/8)
fruit (1/8)

fruit (2/10) mint (3/9) mint (2/8)
toffee (5/8)
fruit (1/8)
toffee (5/9) mint (3/8)
toffee (4/8)
fruit (1/8)
fruit (2/9) mint (3/8)
toffee (5/8)