Sunday, August 21, 2011

A qn in facebook

How many ways I can keep 24 balls into 4 boxes, each box should atleast contain 1 ball, and the total number of balls in the boxes should be 24?
I think the ans is : 24 * 23 * 22 * 21 + (20!); any thoughts?

how did i arrive at this ans?
since its said every box should have atleast 1 ball lets first distribute 1 ball per box i.e.. the total ways of doing this is: 24C1 * 23C1 * 22C1 * 21C1

now i an left with 20 balls. so the question modifies to distributing the 20 balls among 4 boxes any number can go into any box; which is same as saying: i have 20 places distribute 20 balls and the ans is: 20!; hence the answer

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