Combination
Calculate combinations in Grade 9 math using nCr=n!/[r!(n-r)!] to count unordered selections where only which items are chosen matters, not the sequence—like choosing team members.
Key Concepts
Property A combination is a grouping of items where order does not matter. Explanation Think of picking pizza toppings. Choosing mushrooms then pepperoni is the same as pepperoni then mushrooms—you get the same delicious pizza! A combination is just the final group, where the selection order is irrelevant. It’s all about the final set of items you end up with, not the specific path you took to pick them. Examples Choosing 3 friends from a group of 5 to go to the movies is a combination because the group {Ann, Bob, Cid} is the same as {Bob, Cid, Ann}. Selecting 2 side dishes from 6 options at a restaurant is a combination; mac & cheese and fries is the same as fries and mac & cheese. Picking 4 markers from a box of 8 to color a map is a combination since the handful of markers is the same regardless of picking order.
Common Questions
What is a combination and how does it differ from a permutation?
A combination counts unordered selections of items where only which items are chosen matters. For combinations, ABC and BAC are the SAME group. The formula is nCr = n! / [r!(n-r)!], dividing by r! to remove order.
How do you calculate 8C3 (combinations of 8 items taken 3 at a time)?
Apply nCr = n! / [r!(n-r)!]: 8C3 = 8! / [3! × 5!] = (8 × 7 × 6) / (3 × 2 × 1) = 336 / 6 = 56. There are 56 ways to choose 3 items from 8 when order doesn't matter.
When should you use a combination versus a permutation?
Use combinations when selecting a group and order does not matter (choosing committee members, pizza toppings). Use permutations when order matters (rankings, sequences, codes). The key question: does switching the order give a different result?