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