To find the probability distribution for \(S\), we list all possible combinations of 3 discs from the set \{1, 2, 4, 6, 7\}.

The possible combinations are: 124, 126, 127, 146, 147, 167, 246, 247, 267, 467.

For each combination, we determine the smallest number, \(S\).

Counting the occurrences of each smallest number:

• \(S = 1\): 124, 126, 127, 146, 147, 167 (6 combinations)
• \(S = 2\): 246, 247, 267 (3 combinations)
• \(S = 4\): 467 (1 combination)

The total number of combinations is 10.

The probability distribution is calculated as follows:

• \(P(S=1) = \frac{6}{10}\)
• \(P(S=2) = \frac{3}{10}\)
• \(P(S=4) = \frac{1}{10}\)