Marble problem doubt

#1

In marbles problem why we not calculate ncr for those different marbles . We calculate only for same marbles .

#2

@divesh2000 by different marbles you mean marbles of different color. You are asking why are we not doing like, lets select 1 from color 1, 2 from color 2 ,…x from color k. next consider 2 from color 1, 1 from color 2,…
Something like this?
In this we can have many possible combinations and actually given that we do not distinguish between the marbles of same color, so this would be the answer.

#3

we have given 30 marbles and we select 7 marbles of different colours and rest of the marbles can be same or different colour .
Now , for selecting 7 differnet marbles from 30 marbles there are 30C7 possiblities.
why we can’t perform 30C7?
We are only focusing on other 23 marbles.
Please clear this logic.

#4

waiting for your reply sir.

#5

@divesh2000 If we need to choose only 1 marble of K colors from marbles of color n, then this is okay. But our problem is different, here we do not have marbles in n colors, but we have marbles in K colors, and we need to select n marbles such that we atleast have one marble, our problem is opposite of the situation where nCk would work.
Suppose
a+b+c=n
a>1,b>1,c>1
How many possible triplets are the answer of this equation? Consider only positive integer.
You might have done these type of problems in during 11th, 12th. If not no need to worry about.
This question uses similar concept, search about it and study a bit you will get good understanding.

1 Like
#6

Thanks a lot for the explanation.