The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p, and c respectively. Of these subjects, the student has 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. Following relations are drawn in m, p, c :

$$\left( I \right)\,p + m + c = {{27} \over {20}}$$

$$\left( {II} \right)\,p + m + c = {{13} \over {20}}$$

$$\left( {III} \right)\,\left( p \right) \times \left( m \right) \times \left( c \right) = {1 \over {10}}$$