#### 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) 4C3 x 36C2 Option 4) 4C3 x 32C3

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 .

- wherein

Coefficient of  in .

150 marks

Thus,

We get

solutions

and the two papers can be chosen in  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.