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6.3.2613 people on a softball team show up for a game.(C) of the 13 people who show up, three are women. How many ways are there to choose 10 players to take the field if at least one of these players must be a woman?

Question

6.3.26

13 people on a softball team show up for a game.

(C) of the 13 people who show up, three are women. How many ways are there to choose 10 players to take the field if at least one of these players must be a woman?

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Step 1

Consider the provided statement that there are 13 people on a softball team. Out of which 3 are women. Here it is required to choose 10 players with at least one player must be a woman.

Step 2

Total numbers of ways for choosing 10 players out of 13 players, such that at least one player must be a woman is:

C(3,1)x C(10,9)+C(3,2) x C (10,8)+ C(3,3) x C (10, 7)
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C(3,1)x C(10,9)+C(3,2) x C (10,8)+ C(3,3) x C (10, 7)

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Step 3

The above notation can...

10!
10!
=3 x
9!
10!
3x
-+1x
8!2!
7!3!
10 x 9
10x9x8
=3 x10 3x
2x1
3 x 2 x1
=30+135 120
285
help_outline

Image Transcriptionclose

10! 10! =3 x 9! 10! 3x -+1x 8!2! 7!3! 10 x 9 10x9x8 =3 x10 3x 2x1 3 x 2 x1 =30+135 120 285

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