Hi friends, Consider the question In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three postMessage 1 of 1 , Nov 15, 2005View Source
Consider the question
In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
A. 5 C 3
B. 5 P 3
The correct choice is (D) and the correct answer is 3^5.
And this solution
The first letter can be posted in any of the 3 post boxes. Therefore, it has 3 choices.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is 3*3*3*3*3= 3^5
This solution seems perfectly logical.
Now consider this solution
You can model the situation as follows:
Where the | | represent boxes and the * represent letters.
In the above diagram we have 3, 0, and 2 marbles in the three boxes, respectively.
Now this diagram must begin and end with a | but otherwise the two remaining |'s and five *'s can be arranged in any order, and each of these orders is considered equally likely.
So we have 7 objects to arrange in every possible way, 2 of one kind being alike and 5 of a second kind being alike. This can be done in:
------ = C(7,2) = 21 ways.
Can any one tell the flaw in the second method…?