Question 1152128
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Number of possible choices of 2 doughnuts out of the 5: 5 choose 2.<br>
Number of possible choices of 1 out of the 3 cream-filled doughnuts AND 1 of the 2 others: (3 choose 1) times (2 choose 1).<br>
P(1 cream-filled) = {{{(C(3,1)*C(2,1))/C(5,2) = (3*2)/10 = 3/5}}}<br>
Alternate solution method:<br>
P(one cream-filled and one not)
= P((cream-filled first AND not cream-filled second) OR (not cream-filled first AND cream-filled second))
 = {{{(3/5)(2/4)+(2/5)(3/4) = 6/20+6/20 = 12/20 = 3/5}}}<br>