Probability of Selection Calculation

The problem asks for the probability that salesman A is selected when a three-member delegation is chosen from five salesmen (A, B, C, D, E).

Calculating Probability of A's Selection

We can find the probability that A is selected by first calculating the probability that A is *not* selected and then using the complement rule.

Consider the selection process step-by-step. There are 3 positions in the delegation.

• The probability that A is not chosen for the first position is $\frac{4}{5}$ (since there are 4 other salesmen).
• Given A was not chosen first, the probability that A is not chosen for the second position is $\frac{3}{4}$ (3 salesmen left out of 4 remaining).
• Given A was not chosen in the first two positions, the probability that A is not chosen for the third position is $\frac{2}{3}$ (2 salesmen left out of 3 remaining).

The overall probability that A is not selected is the product of these probabilities:

$P(\text{A not selected}) = \frac{4}{5} \times \frac{3}{4} \times \frac{2}{3}$

$P(\text{A not selected}) = \frac{24}{60} = \frac{2}{5}$

Now, we use the complement rule to find the probability that A *is* selected:

$P(\text{A selected}) = 1 - P(\text{A not selected})$

$P(\text{A selected}) = 1 - \frac{2}{5}$

$P(\text{A selected}) = \frac{5}{5} - \frac{2}{5} = \frac{3}{5}$

Therefore, the probability that salesman A gets selected is $\frac{3}{5}$.