Question

When six 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.)

Answer 1

Six basketball players randomly select the order in which they shoot in a free-throw competition.

Let us first calculate all the possible combinations in which the players can arrange them for the throw.

• For choosing the first player there are 6 possible players. Hence, the number of choices of players is 6.
• As the first player is already chosen, now 5 players are remaining and we have to choose any one of them for the second throw. Hence, the number of choices for the second position is 5.
• Now 2 players have already been chosen. Hence, for the third throw number of possible choices is 4.
• Similarly, for the fourth throw, the number of remaining choices is 3.
• For the fifth throw, the number of remaining choices is 2.
• At last, only one player is remaining for the throw. Hence, only 1 possible way of choosing a player.

Hence, the total number of possible combinations in which the players can make throws is 6*5*4*3*2*1 = 6!

It is given that each player has a different name. If we arrange them all in alphabetical order then there is a unique combination in which they can be arranged.

According to the empirical definition of probability of an event,

where n(A) is the number of ways an event A can occur and n(S) is the total number of possible events.

P(shoot free throws in alphabetical order) = = = 0.0013888 = 0.014

Hence, the probability that the players shoot free throws in alphabetical order is 0.014.

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