There are 20 players on a soccer team. From them, a captain and an alternate captain have to be chosen. How many possibilities a

Question

3 years ago

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1 answer:

tester [92] · Answer 1 · 2022-04-21T22:34:04+03:00

Answer:

190 possibilities.

Step-by-step explanation:

The problem is called 20 choose 2, given by the formula for combinations

C(20,2) = 20! / (2! (20-2)!) = 190

alternatively, we can reason it this way:

there are 20 choices to choose a captain and 19 choices for an alternate captain for a total of 380 ways.

However, there are 20 choices to choose an alternate captain and 19 choices for a captain for a total of 380 ways.

Since we are essentially double counting every choice of the posts, we need to divide 380 by 2 to get 190 ways.