1. **Problem statement:** We have a basket with 8 mangoes, 4 oranges, and 2 mangosteen. We want to find the number of ways to pick 4 fruits simultaneously. **Step 1:** Calculate total fruits: $$8 + 4 + 2 = 14$$. **Step 2:** Use the combination formula for choosing $k$ items from $n$ items: $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$. **Step 3:** For 1.1 (no conditions), number of ways to pick 4 fruits from 14 is: $$\binom{14}{4} = \frac{14!}{4!10!}$$ Calculate: $$\binom{14}{4} = \frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1} = \frac{24024}{24} = 1001$$. **Step 4:** For 1.2 (only oranges), since there are 4 oranges, and we want to pick 4, the number of ways is: $$\binom{4}{4} = 1$$. **Answer:** 1.1 Number of ways = 1001 1.2 Number of ways = 1