Question

when eight basketball players are about to have a free - throw competition, they often draw names out of a hat to randomly select the order in which they shoot. what is the probability that they shoot free throws in alphabetical order? assume each player has a different name.
p(shoot free throws in alphabetical order)=
(type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total number of orders

The number of permutations of \(n\) distinct objects is \(n!\). Here \(n = 8\), so the total number of ways to order the 8 basketball - players is \(n!=8! = 8\times7\times6\times5\times4\times3\times2\times1=40320\).

Step2: Determine favorable number of orders

There is only 1 way for the 8 players to shoot in alphabetical order.

Step3: Calculate probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P=\frac{1}{8!}=\frac{1}{40320}\).

Answer:

\(\frac{1}{40320}\)