1. **Problem statement:** We have 7 players with points: 34, 14, 12, 11, 9, 7, 5. We want to find the number of possible samples of size 5 drawn from these 7 players. 2. **Formula for combinations:** The number of ways to choose $k$ samples from $n$ items is given by the combination formula: $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$ 3. **Calculate number of samples:** Here, $n=7$ and $k=5$, so $$\binom{7}{5} = \frac{7!}{5!\times(7-5)!} = \frac{7!}{5!\times 2!}$$ 4. **Simplify factorials:** $$\frac{7\times6\times\cancel{5!}}{\cancel{5!}\times 2\times1} = \frac{7\times6}{2} = 21$$ 5. **List all possible samples:** The 21 samples are all 5-player combinations from the 7 players: - (34,14,12,11,9) - (34,14,12,11,7) - (34,14,12,11,5) - (34,14,12,9,7) - (34,14,12,9,5) - (34,14,12,7,5) - (34,14,11,9,7) - (34,14,11,9,5) - (34,14,11,7,5) - (34,14,9,7,5) - (34,12,11,9,7) - (34,12,11,9,5) - (34,12,11,7,5) - (34,12,9,7,5) - (34,11,9,7,5) - (14,12,11,9,7) - (14,12,11,9,5) - (14,12,11,7,5) - (14,12,9,7,5) - (14,11,9,7,5) - (12,11,9,7,5) 6. **Calculate means for each sample:** Mean is sum of points divided by 5. For example, for (34,14,12,11,9): $$\frac{34+14+12+11+9}{5} = \frac{80}{5} = 16$$ Calculating all means: - 16 - 15.8 - 14.4 - 14.4 - 13.8 - 13.4 - 13 - 12.8 - 12.2 - 11.4 - 14.6 - 14.2 - 13.8 - 13.4 - 13.2 - 12.6 - 12.2 - 11.8 - 11.4 - 11 - 8.8 7. **Construct sampling distribution:** The sampling distribution of the sample means is the list of these means with their frequencies. 8. **Histogram:** The histogram would plot these means on the x-axis and their frequencies on the y-axis, showing the distribution shape. **Final answer:** - Number of possible samples: 21 - Sampling distribution consists of the 21 means listed above.