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I have a doubt, kindly clarify. There are three papers of 100 marks each in an examination. Then the number of ways a student gets 150 marks such that he gets at least60% in two papers.

There are three papers of 100 marks each in an examination. Then the number of ways a student gets 150 marks such that he gets at least 60% in two papers.

  • Option 1)

    3C2 x 32C2

  • Option 2)

    4C3 x 32C2

  • Option 3)

    4Cx 36C2

  • Option 4)

    4Cx 32C3

 
Answers (1)
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As learnt in

Theorem of Combinations -

The number of combinations of n distinct objects taken r at a time when any object may be repeated any number of times is ^{n+r-1}c_{r}.

- wherein

Coefficient of x^{r} in (1-x)^{-n}.

 

 

150 marks

x+y+z=150

x \geqslant60

y \geqslant60

z \geqslant 0

Thus, x'+y'+z'=30

We get 

^{30+3-1}C_{3-1}=^{32}C_{2} \:  solutions

and the two papers can be chosen in ^{3}C_{2} ways.

 


Option 1)

3C2 x 32C2

This option is correct.

Option 2)

4C3 x 32C2

This option is incorrect.

Option 3)

4Cx 36C2

This option is incorrect.

Option 4)

4Cx 32C3

This option is incorrect.

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