Of the 10 prizes 5 prizes are of category Platinum 3 of gold and 2 of silver and

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Of the 10 prizes 5 prizes are of category Platinum 3 of gold and 2 of silver and they are placed in an enclosure for an olympiad contest. The prizes are awarded by allowing winners to select randomly from the prizes remaining. When the 8th participant goes to collect the prize what the probability that last 3 prizes are 1 of platinum 1 of gold and 1 of silver?

Options:

A . 15

B . 14

C . 13

D . 110

Answer: Option B
:
B
Sample space:

^{10} C_{7}

. because 7 prizes have already been selected= 120.
Favorable:

^{5} C_{4} \times^{3} C_{2} \times^{2} C_{1} = 30

.
P(E)=

\frac{30}{120} = \frac{1}{4}

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