Kenneth Rosen Edition 6th Exercise 5.5 Question 38 (Page No. 381)

Question

A professor packs her collection of 40 issues of a mathematics journal in four boxes with 10 issues per box.How many ways can she distribute the journals if

(a)each box is numbered, so that they are distinguishable?

(b)the boxes are identical so that they cannot be distinguished?

Comments

For first part I think it is distribution of similar objects into distinct boxes

Which happens to use n-1+rCr, n=4, r=10 which gives 13C10.

Is this correct?

For (b) I have no idea.

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No this formula is used when we have choice to put any number of issue in boxes.

Question is simple:

How many ways 40 general put in 4 box such that each contain 10 .

⁴⁰c₁₀ * ³⁰c₁₀ * ²⁰C₁₀ *¹⁰c₁₀

These are number when box are distinct .

IF box are labbled then (⁴⁰c₁₀ * ³⁰c₁₀ * ²⁰C₁₀ *¹⁰c₁₀) / 4!

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@anu

if each must contain 10 was not mentioned then?

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then some other condition will be there.

Plz ask specific question.