There are 10 prizes, five A’s, three B’s and two C’s, placed in identical sealed envelopes for the top 10 contestants in a Mathematics contest. The prizes are awarded by allowing winners to select an envelope at random from those remaining. When the 8th contestant goes to select the prize, the probability that the remaining three prizes are one A, one .B and one C is

# There are 10 prizes, five A's, three B's and two C's, placed in identical sealed envelopes for the top 10 contestants in a Mathematics contest. The prizes are awarded by allowing winners to select an envelope at random from those remaining. When the 8th contestant goes to select the prize, the probability that the remaining three prizes are one A, one .B and one C is

1. A

1/4

2. B

1/3

3. C

1/12

4. D

1/10

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### Solution:

$\begin{array}{l}\mathrm{n}\left(\mathrm{S}\right){=}^{10}{\mathrm{C}}_{7}=120\\ \mathrm{n}\left(\mathrm{A}\right){=}^{5}{\mathrm{C}}_{4}{×}^{3}{\mathrm{C}}_{2}{×}^{2}{\mathrm{C}}_{1}\\ \mathrm{P}\left(\mathrm{E}\right)=\frac{5×3×2}{120}=\frac{1}{4}\end{array}$

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