A dice is thrown six times, it being known that each time a different digit is shown. The probability that a sum of 12 will b e obtained in the first three throws is `5//24` b. `25//216` c. `3//20` d. `1//12`

Options

A. `(5)/(24)`
B. `(25)/(216)`
C. `(3)/(20)`
D. `(1)/(12)`

Answer

C

Explanation

Since it is known that each time a different digit appears, total number of cases is `6!`
The sum in the first three throws is 12 if we get (1, 5, 6), (2, 4, 6) or (3, 4, 5) in any order.
So, number of cases for first three throws = `3 xx 3!` ways.
`therefore` Number of favourable cases = `3 xx 3! xx 3!`
`therefore` Required probability = `(3 xx 3! xx 3!)/(6!) = (3)/(20)`