Question

In a rugby match, a tie at the end of two overtime periods leads to a "shootout" with five kicks taken by each team from the center of the 22-meter line. Each kick must be taken by a different player. How many ways can 5 players be selected from the 15 eligible players? For the 5 selected players, how many ways can they be designated as first, second, third, fourth, and fifth? 5 players can be selected from the 15 eligible players in different ways. Out of those 5 players that are selected, they can be designated as first, second, third, fourth, and fifth in different ways. (Type whole numbers.) Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. The indicated z score is (Round to two decimal places as needed.)

Answer 1

There are 3,003 ways to select 5 players from 15 eligible players and 120 ways to order the selected 5 players into positions.

Step-by-step explanation:

The number of ways 5 players can be selected from 15 eligible players is found using the combination formula C(n, k) = n! / (k!(n-k)!), where 'n' is the total number of players and 'k' is the number of players to be selected.

In this case, C(15, 5) calculates how many combinations of players can be formed. Once 5 players are selected, they can be ordered in 5! different ways because there are 5 positions to fill by 5 players.

For the calculation:

• Number of ways to choose 5 players: C(15, 5) = 15! / (5!(15-5)!) = 15! / (5!10!) = 3,003.
• Number of ways to order 5 players: 5! = 5 x 4 x 3 x 2 x 1 = 120.