Three Mistakes of My Life
The probabilities that a student passes in Mathematics, Physics and Chemistry are \(M\), \(P\) and \(C\) respectively.
Of these subjects, the student has a 75% chance of passing in at least one, a 50% chance of passing in at least two, and a 40% chance of passing in exactly two.
Then for real values of \(x\), find the sum of all coefficients of \(x\) (including the constant term) in the expansion of \((x-M)(x-P)(x-C)\).
Assumptions and Clarifications
- The required sum must also include the constant term.