There are 10 prizes, five As, there Bs and two Cs, 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. Then the 8th contestant goes to select the prize, the probability that the remaining three prizes are once `Aa n dB` and one `C` is `1//4` b. `1//3` c. `1//12` d. `1//10`

Options

A. `1//4`
B. `1//3`
C. `1//12`
D. `1//10`

Answer

A

Explanation

`n(S) = .^(10)C_(7) = 120`
`n(E) = .^(5)C_(4) xx .^(3)C_(2) xx .^(2)C_(1)`
`therefore P(E) = (5xx3xx2)/(120) = (1)/(4)`