Practice Combination in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A combination is an unordered selection of objects — the number of ways to choose items from distinct items is .
How many ways to choose a group? .
Showing a random 20 of 50 problems.
Example 1
easyCompute .
Example 2
mediumFrom 10 marbles (4 red, 6 blue), how many ways to pick 3 marbles with exactly 1 red?
Example 3
easyHow many ways to choose a 4-person subcommittee from a group of 6?
Example 4
mediumA pizza shop offers 10 toppings. How many distinct pizzas use 4 different toppings?
Example 5
mediumFrom 8 people, choose 4 such that two specific people, Bob and Carol, are NOT both included.
Example 6
mediumSolve for : .
Example 7
easyA jar holds 5 different fruits. How many distinct fruit salads of 3 different fruits can be made? (Order does not matter inside a salad.)
Example 8
easyCompute .
Example 9
easyA committee of is to be chosen from people. How many different committees are possible?
Example 10
mediumHow many ways to split 6 distinct items into a chosen group of 4 and leave 2 behind?
Example 11
mediumHow many ways can you choose books from a shelf of books?
Example 12
easyCompute .
Example 13
easyFill in the blank: .
Example 14
mediumHow many diagonals does a convex hexagon (6 vertices) have?
Example 15
mediumHow many 5-card poker hands are there from a 52-card deck?
Example 16
easyUse symmetry to find .
Example 17
easyHow many ways to choose 2 toppings from 5 (order does not matter)?
Example 18
hardA 4-card hand is drawn from a 52-card deck. What is the probability the hand contains all 4 aces?
Example 19
easyHow many ways can a teacher choose 2 students from a class of 9 to be hall monitors?
Example 20
mediumA committee of 3 is chosen from 7 people. How many committees are possible?