m identical balls are to be placed in n distinct bags. You are given that m>=kn,

Question

m identical balls are to be placed in n distinct bags. You are given that m>=kn,where k is a natural number>=1. In how many ways can the balls be placed in the bags if each bag must contain at least k balls?

Explanation / Answer

( m-kn+n-1) ( n-1 ) f there are m (>=kn) balls, we can put k balls in all the bags initially and remaining number of balls are (m-kn). This ensures the fact that there are atleast k balls in each bag. the remaining balls can be put in the following ways, to explain this consider there are A (m-kn) balls and n bags the n bags can be visualized as (n-1) seperaters ('|') Now distributing the A balls is generating string using A identical balls and (n-1) identical seperaters '|'. b b b b.......A times | | | | | ......(n-1) times This can be done in (A+(n-1))! / (A!) ((n-1)!). this is nothing but A C (n-1) {C as in combination} here in the problem A is m-kn.

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.