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illustrate the combinations as in each situation using the formula then solve show your solution in 1.how many ways can 6 ice cream flavors be selected from 12 possible choices?​

Sagot :

PROBLEM:

Illustrate the combinations in each situation using the formula then solve. Show your solution.

  1. How many ways can 6 ice cream flavors be selected from 12 possible choices?

SOLUTION:

We'll gonna use the formula in solving combinations. The C stands for combination, n for the number of objects in a set while r is the number of selected objects.

  • The given are: n = 12 ice cream flavors and r = 6 ice cream flavors.

[tex]\sf_n C_r=\frac{n !}{r ! (n-r) !}[/tex]

[tex]\sf_{12} C_6=\frac{12 !}{6! (12-6) !}[/tex]

[tex]\sf_{12} C_6=\frac{12×11×10×9×8×7×6!}{6! 6 !}[/tex]

[tex]\sf_{12} C_6=\frac{12 ×11×10×9×8×7}{6 !}[/tex]

[tex]\sf_{12} C_6=\frac{12×11×10×9×8×7}{6×5×4×3×2×1}[/tex]

[tex]\sf_{12} C_6=\frac{\cancel{12}×11×\cancel{10}^2×\cancel9^3×\cancel8^2×7}{\cancel{6×5×4×3×2×1}}[/tex]

[tex]\sf_{12} C_6=\frac{11×2×3×2×7}{1}[/tex]

[tex]\sf_{12} C_6=924[/tex]

ANSWER:

There are 924 ways you can select 6 ice cream flavors from 12 possible choices.