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A box contains 10 chocolates, of which 4 are dark chocolates and 6 are milk chocolates.
If two chocolates are randomly selected without replacement, what is the probability
of getting one dark chocolate and one milk chocolate in any order?
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The number of all possible different pairs without looking the order
is the number of combinations of 10 items taken 2 at a time
total = = = 5*9 = 45.
The number of pairs (dark,milk), in this order, is 4*6 = 24;
the number of pairs (milk,dark), in this order, is 6*4 = 24;
but since the order does not matter, we DO NOT ADD 24 + 24 - we simply take/keep the value of 24
for all possible different pairs (dark,milk) or (milk,dark) of favorable pairs
favorable = 6*4 = 24.
The probability under the problem's question is
P = = = . ANSWER
Solved.