a professor packs her collection of 40 issues of a mathe- matics 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 distinguish- able?

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AmitPaswango AmitPaswango · Answer 1

If each box is numbered , so that they are distinguishable , then professor can distribute the journal in 40!/(10! )⁴ ways .

In the question ,

it is given that

the professor had 40 issues of mathematics journal;

number of boxes to be packed in = 4 boxes

number of issues per box = 10 issues

since the 4 boxes are numbered ,

So , in

Box 1 , the 10 issues out of 40 can be packed in ⁴⁰C₁₀ ways .

and

for box 2 the number of issues remaining is 30

So , in Box 2 the 10 issues out of 30 can be packed in ³⁰C₁₀ ways .

for Box 3

the number of issues remaining is 20

so, in box 3 the 10 issues out of 20 can be filled in ²⁰C₁₀ ways .

for Box4

the umber of issues remaining is 10 ,

so , in box 4 the 10 issues out of 10 can be filled in ¹⁰C₁₀ ways .

The journals can be distributed in ⁴⁰C₁₀ × ³⁰C₁₀ × ²⁰C₁₀ × ¹⁰C₁₀ ways

= (40!)/(30! * 10! ) × (30!)/( 20! * 10!) × (20!)/(10! * 10!) × 1

On simplifying further , we get

= 40!/(10! )⁴ ways .

Therefore , If each box is numbered , so that they are distinguishable , then professor can distribute the journal in 40!/(10! )⁴ ways .

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