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IN how many ways we can distribute 10 identical looking pencils to 4 students so that each student get at least one pencil?

a)5040

b)210

c)84

d)none of these

MyApproach

To distribute 10 identical pencils into 4 students,I first gave 4 pencils to 4 students.I am left with 6 pencils to distribute to these 4 students.

How to distribute these pencils to them

Can Anyone guide me how to solve this problem?

justin takro
  • 1,288
  • First pls get a pencil to each student now you have six pencils and four student. now you can solve it easy. – Amir Nov 16 '15 at 04:40

2 Answers2

1

It is basically the same problem as inserting three sticks between ten balls to separate the balls into four positive groups. It is given by the formula ${10-1\choose 4-1}=84$.

More formally it is the number of positive integer solutions of equation

$x_1+x_2+x_3+x_4=10$

And it has the same formula.

cr001
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The formula is $x_1+x_2+x_3+x_4=10$ so we want each one to get one pencil atleast so the general solution is $(n-1)C(k-1)$ here $n=10 and k=4$ so answer is $9C3=84$. Thus option C. Another way to look at is draw 10 pens we have to draw $3$ strokes to create 4 gaps ie children but acc. To condition we cannot place a stroke behind $1st$ pen . So one option is eliminated so we are left with $9$ options. So number of ways are $9C3$ which is again $84$. Thus option C.

Archis Welankar
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