Step 1: Determine the fraction of people who drank mango juice. Let the total number of people be $T$. Fraction of people who drank mango juice $= \frac{3}{8}$. Step 2: Determine the fraction of people remaining after those who drank mango juice. Remainder $= 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8}$ of the total people. Step 3: Determine the fraction of people who drank pineapple juice. Fraction of people who drank pineapple juice $= \frac{1}{4}$ of the remainder. $$= \frac{1}{4} \times \frac{5}{8} = \frac{5}{32}$$ of the total people. Step 4: Determine the fraction of people who drank orange juice. The rest drank orange juice. Fraction of people who drank orange juice $= \text{Remainder} - \text{Fraction for pineapple juice}$ $$= \frac{5}{8} - \frac{5}{32}$$ To subtract these fractions, find a common denominator, which is 32. $$\frac{5}{8} = \frac{5 \times 4}{8 \times 4} = \frac{20}{32}$$ So, the fraction for orange juice $= \frac{20}{32} - \frac{5}{32} = \frac{15}{32}$ of the total people. Step 5: Use the given number of people who drank orange juice to find the total number of people ($T$). We are given that 240 people drank orange juice. $$\frac{15}{32} \times T = 240$$ To find $T$, multiply 240 by the reciprocal of $\frac{15}{32}$: $$T = 240 \times \frac{32}{15}$$ $$T = (240 \div 15) \times 32$$ $$T = 16 \times 32$$ $$T = 512$$ So, there were 512 people in total at the ceremony. Step 6: Calculate the number of people who drank mango juice. Number of people who drank mango juice $= \frac{3}{8}$ of the total people. $$= \frac{3}{8} \times 512$$ $$= 3 \times (512 \div 8)$$ $$= 3 \times 64$$ $$= 192$$ The number of people who drank mango juice is $\boxed{192}$. Last free one today — make it count tomorrow, or type /upgrade for unlimited.