probability

9 balls :
5 odd numbers : 1, 3, 5, 7 , 9
4 even numbers : 2, 4, 6, 8

Number of ways to draw 2 balls without restriction
= 9C2
= 9!/2!7!
= 36

Number of ways to draw 2 balls that the product of the numbers is even
= Number of ways to draw (1 odd number and 1 even number) or (2 even number)
= 5C1 x 4C1 + 4C2
= (5!/1!5!) x (4!/1!3!) + (4!/2!2!)
= 5 x 4 + 6
= 26

The required probability
= 26/36
= 13/18

2013-11-16 00:32:10 補充：
1 和 2 當作一個組合，不計次序。

P(1st ball is odd) = 5/9.
P(2nd ball is odd) = 4/8.
P(Product of 2 balls drawn are even) = 1 - P(1st ball is odd) x P(2nd ball is odd)
= 1 - (5/9)(4/8) = 1 - 5/18 = 13/18.

Probability=(9*8-4*5)/(9*8)=13/18