A school has five houses A, B,C,D and E. A class has 23 students, 4 from houses A, 8 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

Options

A. `(4)/(23)`
B. `(6)/(23)`
C. `(8)/(23)`
D. `(17)/(23)`

Explanation

To solve the problem, we need to find the probability that a randomly selected student is not from houses A, B, and C. Let's break it down step by step.

### Step 1: Determine the total number of students in the class.
The total number of students in the class is given as 23.

### Step 2: Identify the number of students from each house.
- Students from house A = 4
- Students from house B = 8
- Students from house C = 5
- Students from house D = 2
- Students from house E = (Total students - Students from A, B, C, D)

### Step 3: Calculate the number of students from house E.
First, we need to find the total number of students from houses A, B, C, and D:
- Total from A, B, C, and D = 4 (A) + 8 (B) + 5 (C) + 2 (D) = 19

Now, we can find the number of students from house E:
- Students from house E = Total students - Total from A, B, C, D
- Students from house E = 23 - 19 = 4

### Step 4: Determine the number of students not from houses A, B, and C.
We need to find the students who are not from houses A, B, and C:
- Students not from A, B, and C = Students from D + Students from E
- Students not from A, B, and C = 2 (D) + 4 (E) = 6

### Step 5: Calculate the probability.
The probability that a randomly selected student is not from houses A, B, and C is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

In this case:
- Number of favorable outcomes (students not from A, B, and C) = 6
- Total number of outcomes (total students) = 23

Thus, the probability is:
\[ \text{Probability} = \frac{6}{23} \]

### Final Answer:
The probability that the selected student is not from houses A, B, and C is \( \frac{6}{23} \).

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