5. Sixteen peopleon a softball team show up for a game.a) How many ways are there to choose 9 players to take the field?b) How many ways are there to assign the 9 positions by selecting players from the 16people who show up?c) Of the 16 people who show up, 7 are women. How many ways are there to choose 9players to take the field if at least one of these players must be a woman?

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Asked Jul 8, 2019
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5. Sixteen people
on a softball team show up for a game.
a) How many ways are there to choose 9 players to take the field?
b) How many ways are there to assign the 9 positions by selecting players from the 16
people who show up?
c) Of the 16 people who show up, 7 are women. How many ways are there to choose 9
players to take the field if at least one of these players must be a woman?
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5. Sixteen people on a softball team show up for a game. a) How many ways are there to choose 9 players to take the field? b) How many ways are there to assign the 9 positions by selecting players from the 16 people who show up? c) Of the 16 people who show up, 7 are women. How many ways are there to choose 9 players to take the field if at least one of these players must be a woman?

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Expert Answer

Step 1

(a)

Total number of people that show up for game is 16.

Therefore, number of ways for choosing 9 players out of 16 is:

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16! 1°C9 91(16-9) 16! 9!7! 16 x15x14x13x12 x1 1x 10 7x6x5x 4x3x 2x1 57657600 5040 -11440

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Step 2

Thus, the total number of ways for choosing 9 players out of 16 is 11440.

 

(b)

Now, total number of ways for assigning 9 players out of 16 is:

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16! 16p (16-9) 16! 7! 16x15x14x13 x12 x1 1x10 x9x8 =4151347200

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Step 3

Thus, number of ways for assigning 9 players out of 16 is 4151347200.

 

(c)

Now, it is given that, out of 16 people, 7 are women

Now, total number of ways for choosing 9 players out of 16...

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(ТCо*С) 16C9 -16с9-("со 9! 7! 11440 0!(7-0) 9!(9-9)! 7!9! =11440- (7)' 9! =11440 =11439 9с

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