A box contains 10 balls numbered from 0 to 9. The balls are identical, so when Karan starts picking a ball out of the bag, he is equally likely to pick anyone of them. Karan picked a ball and replaced it in the bag after noting its number. He repeated this process 2 more times.
What is the probability that the ball picked first is numbered higher than the ball picked second and the ball picked second is numbered higher than the ball picked third?
A box contains 10 balls numbered from 0 to 9. The balls are identical, so when Karan starts picking a ball out of the bag, he is equally likely to pick anyone of them. Karan picked a ball and replaced it in the bag after noting its number. He repeated this process 2 more times.
What is the probability that the ball picked first is numbered higher than the ball picked second and the ball picked second is numbered higher than the ball picked third?
The correct option is A
Let the number on the ball picked first = a, second = b and third = c.
The three numbers a,b and c are distinct.
Three distinct balls can be picked in (10 × 9 × 8) ways.
The order of a, b and c can be as follows:
(i) a > b > c ;
(ii) a > c > b ;
(iii) b > c > a ;
(iv) b > a > c ;
(v) c > a > b ;
(vi) c > b > a
They will occur equal number of times.
Thus, the number of ways in which (a > b > c) = 10C3 = 120
∴ Required probability = 10C3103 = 325
Let the number on the ball picked first = a, second = b and third = c.
The three numbers a,b and c are distinct.
Three distinct balls can be picked in (10 × 9 × 8) ways.
The order of a, b and c can be as follows:
(i) a > b > c ;
(ii) a > c > b ;
(iii) b > c > a ;
(iv) b > a > c ;
(v) c > a > b ;
(vi) c > b > a
They will occur equal number of times.
Thus, the number of ways in which (a > b > c) = 10C3 = 120
∴ Required probability = 10C3103 = 325
