Eight persons A, B, C, D, E, F, G and H appeared for an inter view. Find the probability that both A and D are selected in the interview?

Answer

To solve the problem of finding the probability that both A and D are selected in the interview among the 8 persons, we can follow these steps:

### Step 1: Understand the total number of persons
We have a total of 8 persons: A, B, C, D, E, F, G, and H.

### Step 2: Determine the total outcomes
The total number of ways to select any 2 persons from these 8 is given by the combination formula \( C(n, r) \), where \( n \) is the total number of persons and \( r \) is the number of persons to select. Here, we need to select 2 persons from 8.

\[ \text{Total outcomes} = C(8, 2) = \frac{8!}{2!(8-2)!} = \frac{8 \times 7}{2 \times 1} = 28 \]

### Step 3: Determine the favorable outcomes
The favorable outcomes for our event (both A and D being selected) is just 1, since there is only one specific combination of A and D.

### Step 4: Calculate the probability
The probability \( P \) of both A and D being selected is given by the formula:

\[ P(\text{A and D selected}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{28} \]

### Final Answer
Thus, the probability that both A and D are selected in the interview is \( \frac{1}{28} \).

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