Question

A box contains 10 balls numbered 1 through 10. Anuj, Anisha and Amit pick a ball each, one after the other, each time replacing the ball. What is the probability that Anuj picks a ball numbered less than that picked by Anisha, who in turn picks a lesser n

Answer 1

Solution:-
The balls are numbered 1, 2, 3, 4 ,5, 6, 7, 8, 9 and 10.
If 1 numbered ball is picked up by Anuj then Anisha will pick up 2, 3, 4, 5..... or 10 = 9 ways.
Like this,
2 numbered .................. = 8 ways
3 numbered .................. = 7 ways
.
.
.
.
.
9 numbered ................... = 1 way
So, the number of ways that Anuj picks a ball numbered less than that picked by Anisha = 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45 ways
Amit picked a ball from remaining 8 ball = 8c₁ = 8 ways
One ball lesser from 3, that is 3c₁
Number of possible ways = (45*8)/3
360/3 = 120 ways
Total number of possible ways = 10c₁*10c₁*10c₁ = 1000 ways
So, the probability = 120/1000
= 3/25
Answer.