"Thirteen people on a softball team show up..." was answered by students like you

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Algebra
Pre-Algebra
Factors and multiples

generals336

Answered question

2021-10-19

Thirteen people on a softball team show up for a game. How many ways are there to choose 10 players to take the field?

Answer & Explanation

Ayesha Gomez

Skilled2021-10-20Added 104 answers

We are interested in choosing 10 players from the 13 people on the softball team that show up for a game.
$n = 13$
$r = 10$
The order in which the players are selected doesn't matter, as a different order of the players results in the same players taking the field, and thus we should use the definition of a combination.
Number of ways $= C (13, 10)$
$= \frac{13!}{10! (13 - 10)!}$
$= \frac{13!}{10! 3!}$
$= \frac{13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot \dots \cdot 1}{10 \cdot 9 \cdot \dots \cdot 1 \cdot 3 \cdot 2 \cdot 1}$
$= \frac{13 \cdot 12 \cdot 11}{3 \cdot 2 \cdot 1}$
$= 13 \cdot 2 \cdot 11$
$= 286$
Thus there are 286 ways to choose 10 players to take the field.

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