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Yolanda scored 10 points in a basketball game. She could have scored with one-point free throws, two-point field goals, or three-point field goals. In how many different ways she could have scored her 10 points?

Sagot :

The points scored in the game is an illustration of combinations. She could have scored the 10 points in 302400 ways.

The given parameters are

[tex]n = 10[/tex] ---- total points

[tex]r_1 = 1[/tex] ---- one-point free throw

[tex]r_2 = 2[/tex] --- two-point field goals

[tex]r_3 = 3[/tex] --- three-point field goals

The number of ways (k) she could have scored the points is:

[tex]k = \frac{n!}{r_1 ! \times r_2! \times r_3 !}[/tex]

So, we have:

[tex]k = \frac{10!}{1 ! \times 2! \times 3 !}[/tex]

Solve each factorial

[tex]k = \frac{3628800}{1 \times 2 \times 6}[/tex]

[tex]k = \frac{3628800}{12}[/tex]

Evaluate

[tex]k = 302400[/tex]

Hence, she could have scored the 10 points in 302400 ways.

Read more about combinations at:

https://brainly.com/question/15301090