Question

when five 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 \(n = 5\), so the total number of ways to order the 5 basketball - players is \(n!=5!=5\times4\times3\times2\times1 = 120\).

Step2: Determine favorable number of orders

There is only 1 way for the 5 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 \(P=\frac{1}{120}\).

Answer:

\(\frac{1}{120}\)