Question

There are eleven people on a softball team and nine different positions. work through the questions to determine how many ways a coach can choose the players for the positions if amy does not want to pitch. if there are eleven people on the team and nine positions, how many total arrangements of the players can be made? if amy does not want to play pitcher, then there are now people available to pitch. assuming the pitcher has already been chosen, there are ten remaining players and remaining positions. how many ways are there to arrange the remaining players and positions?

Answer 1

Permutation helps us to know the number of ways an object can be arranged in a particular manner. The number of ways the remaining player can be arranged is 1,814,400.

What is Permutation?

Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

$^nP_r = \dfrac{n!}{(n-r)!}$

where,

n is the number of choices available,

r is the choices to be made.

Given that the team has 11 players while there are only 9 positions available, therefore, the number of ways the coach can choose 9 people and arrange them is,

$^{11}P_9 = \dfrac{11!}{(11-9)!} = \dfrac{11!}{2!} = 19,958,400$

Now, since Amy does not want to be a pitcher, therefore, the number of ways the remaining people can be arranged in the place of the pitcher is 10.  Also, the position remaining in the team is 8, while the number of people remaining is 10. Thus, the number of ways the remaining people can be arranged are,

$\text{Number of ways}= ^{10}P_8 =\dfrac{10!}{(10-8)!} = 1,814,400$

Hence, the number of ways the remaining player can be arranged is 1,814,400.

Learn more about Permutation:

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Answer 2

Answer:

1: 19,958,400

2: 10

3: 1,814,400

Step-by-step explanation: