Permutations,combinations Plus Probability...Some Awesome questions

[SINGHAM]

Hi, RAJ!

I would like first to play with small numbers.

1.Suppose you have 10 identical balls and you want to distribute among 3 persons so that each gets at least 2.So, balls: Undistiguishible, men: distinguishible. What is the first response of your mind is? As all of the balls are identical, no matter which ball is got by whom. So, simply you will first distribute 2 balls each of 3 person. Now you are left with 4 balls. And you have no restriction in distribution, i.e, you can give no ball to a particular person. So, the problem can also be stated as if there are 7 balls and we have to distribute them as each gets at least one ball. Why? because, after distributing 7 balls  as each gets at least one ball, if we take 1 ball from each, we are left with the solution of the original problem: 4 balls and 3 men with no distributional restriction. So, simply the answer is 6C2.

2.Suppose you have 10 identical balls and you want to distribute among 3 persons. So, balls: Undistiguishible, men: distinguishible. Similar as above! We can think this problem as 13 balls, 3 men, each gets at least 1 ball. So, 12C2.

Now go to the original problem

[RajEco]

Thanks man :)