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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:
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