A watch of meritorius students of the coaching institute is to be formed. For this a student must obtain at least 80% aggregate marks in a test of Physics, Chemistry and Math. (M.M. = 100 each).
The number of ways in which a student can qualify for the batch of meritorius students is

The correct answer is: (101)³ – ²⁴²C₂₃₉

p + c + m 240…(1)
p + c + m < 240…(2)
where p, c, m denote the physics, chemistry and mathematics resp.

Positive integral solution of (3)
= number of integral solution of inequality (2)
= co-eff. of ²⁴⁰ in
= co-eff. of ²³⁹ in
= 239 + 4 – 1 = ²⁴²C₂₃₉
Total number of C₂₃₉ ways of scoring maths
= 101 101 101 = (101)³[marks can be 0, 1, 2, … 100]
\ number of ways = (101)³ – ²⁴²C₂₃₉