Question:
A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D and rest from
house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from A, B and C is
(a) $\frac{4}{23}$
(b) $\frac{6}{23}$
(c) $\frac{8}{23}$
(d) $\frac{17}{23}$
Solution:
(b) Total number of students = 23
Number of students in house A, B and C = 4+ 8 + 5 = 17
$\therefore \quad$ Remains students $=23-17=6$
So, probability that the selected student is not from $A, B$ and $C=\frac{6}{23}$