When four basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select th alphabetical order? Assume each player has a different name. P(shoot free throws in alphabetical order) (Type an integer or a simplified fraction.)

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To determine the probability that the four basketball players shoot free throws in alphabetical order, we can use the principles of probability and permutations.

1. **Total Possible Orders:**
   - Since there are four players, each with a distinct name, the total number of possible shooting orders is given by the number of permutations of four distinct elements.
   - This is calculated as $$4! = 4 \times 3 \times 2 \times 1 = 24$$.

2. **Favorable Outcome:**
   - There is only **one** specific order where the players are shooting in exact alphabetical order.

3. **Probability Calculation:**
   - The probability $$P$$ is the ratio of the number of favorable outcomes to the total number of possible outcomes.
   $$
   P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{1}{24}
   $$

**Final Answer:**

$$\boxed{\dfrac{1}{24}}$$
The probability that the four basketball players shoot free throws in alphabetical order is $$\frac{1}{24}$$.

When four basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select th alphabetical order? Assume each player has a different name. P(shoot free throws in alphabetical order) (Type an integer or a simplified fraction.)

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