An lce chest contains 6 cans of apple Juice, 4 cans of grape Juice, 4 cans of orange Juice, and 8 cans of mango Julce. Suppose that you reach Into the container and randomly select three cans in succession. Find the probability of selecting three cans of apple Julce. The probability of selecting from the lce chest three cans of apple julce is (Type an integer or a simplified fraction.)

To find the probability of selecting three cans of apple juice in succession, we first calculate the total number of juice cans. There are 6 cans of apple juice, 4 cans of grape juice, 4 cans of orange juice, and 8 cans of mango juice, resulting in a total of \(6 + 4 + 4 + 8 = 22\) cans. The probability of selecting the first can of apple juice is \(\frac{6}{22} = \frac{3}{11}\). After selecting one can, there are now 5 cans of apple juice left and 21 total cans. Thus, the probability for the second selection is \(\frac{5}{21}\). For the third selection, the probability becomes \(\frac{4}{20} = \frac{1}{5}\). Now, we multiply these probabilities together: \[ P(3 \text{ apple juices}) = \frac{3}{11} \times \frac{5}{21} \times \frac{1}{5} = \frac{3}{11 \times 21} = \frac{3}{231} = \frac{1}{77} \] So, the probability of selecting three cans of apple juice is \(\frac{1}{77}\).