Nine marbles numbered 1 to 9 are placed in a barrel and three are drawn out, without replacement. Determine -:

1. The probability that the three digit number formed from the marbles in the order drawn is divisible by (a) Five (b) Seven (c) Nine.
2. The probability that a three digit number can be formed by rearranging the marbles drawn, that is divisible by (a) Five (b) Seven (c) Nine.

To be divisible by 5, the last digit must be 5 (there is no 0). So the first 2 digits cannot be 5.

Prob. of 1'st digit not equal to 5 = 8/9

prob. of 2'nd digit not equal to 5 = 7/8

prob. of 3'rd digit equal to 5 = 1/7

result is 8/9 * 7/8 * 1/7  =  1/9

 

Posted by ruti on 2006-05-01 16:26:19