Twelve trophies are baseball,
eight are football and
five are basketball.
At random what is the probability of pulling one basketball and two baseball trophies from boxes
There are 5 ways of pulling out one basketball
and 12C2 = 66 ways of pulling out 2 baseball ones $${\left({\frac{{\mathtt{12}}{!}}{{\mathtt{2}}{!}{\mathtt{\,\times\,}}({\mathtt{12}}{\mathtt{\,-\,}}{\mathtt{2}}){!}}}\right)} = {\mathtt{66}}$$
Now the total number of ways three trophies can be pulled out is 25C3 =2300
$${\left({\frac{{\mathtt{25}}{!}}{{\mathtt{3}}{!}{\mathtt{\,\times\,}}({\mathtt{25}}{\mathtt{\,-\,}}{\mathtt{3}}){!}}}\right)} = {\mathtt{2\,300}}$$
So P(1 basketball and 2 baseball) = (5*66)/2300 approx 0.14
$${\frac{{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{66}}}{{\mathtt{2\,300}}}} = {\frac{{\mathtt{33}}}{{\mathtt{230}}}} = {\mathtt{0.143\: \!478\: \!260\: \!869\: \!565\: \!2}}$$
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