## johnny5520 3 years ago One is looking to invest 15 thousand dollars among 5 opportunities. Each investment should be an integral in units of 500 dollars. A portfolio corresponds to an investment policy. For example, (5,6,3,6,10) is a portfolio that invests 5 units in the first opportunity, 6 units in the second, 3 units in the third, 6 units in the fourth and 10 units in the fifth opportunity. (0,14,8,8,0) is another portfolio in which no investment is made in the first and fifth opportunities. The total number of portfolios that invests at least one unit in each of the first three opportunities is:

1. johnny5520

theres 3 questions i posted, all similar

2. shaan_iitk

its like how many ways to distribute 30 sweets between 5 kids so that 3 of them get atleast 1 ...

3. johnny5520

yeah how to do that

4. shaan_iitk

the way to do this is to say distribute 3 sweets initially to those 3 kids .. so now we are left with 27 sweets .. so basically you have to find number of ways to distribute 27 sweets among 5 kids ... this would be 27c5

5. johnny5520

ah ok, ive gotta restart my computer, could you take a look at the rest?

6. johnny5520

hey shaan why is it 27c5? how would 27c5 give the number of ways it can be distributed

7. shaan_iitk

sorry in haste I miscalculated .. .look u need to distribute 27 sweets among 5 kids. Imagine you have to arrange 27 women and 5 men. How many ways can you do it ?? 32!/(5!*27!) ... now say I make a condition that the last person would be a man then how many ways --> 31!/(27!*4!) .. Now say I say that any women which comes to the left of a man is given to him then I am through right??