How many choices do I have? This lesson can help you with answering this question! Combination is the process of selecting members from a set of items. Combination formula is your best friend in this lesson. Unlike permutations, order doesn't matter in combinations!
Combination: nCr = number of selections of r items taken from a set of n distinct items (order does NOT matter!!)
Compare the difference between the following 2 scenarios:
How many ways can a president, a vice president, and a treasurer be selected from a class of 20 students?
How many different committees of 3 people can be selected from a class of 20 students?
A standard deck of 52 cards consists of:
• 4 suits: diamonds, hearts, spades, and clubs
• each suit has 13 cards
• red cards: diamonds and hearts
• black cards: spades and clubs
• face cards: Jacks, Queens, and Kings
How many different 5-card hands can be formed containing:
any 5 cards (no restrictions)?
all black cards?
1 black card and 4 red cards?
all face cards?
3 Jacks and 2 Kings?
Problems with "at least", "at most"
From a standard deck of 52 cards, how many different 5-card hands can be formed containing:
exactly 2 Diamonds?
at least 2 Diamonds?
at most 2 Diamonds?
There are 20 members in a student council, 7 boys and 13 girls. How many ways can a committee of 5 people be selected if there must be:
at least 3 boys?
at most 1 girl?
at least 1 girl?
at least 2 boys and 2 girls?
Five points are marked on a circle. By connecting the points on the circle,
How many triangles can be formed?
How many line segments can be formed
Form a pentagon inside the circle by connecting the 5 points. How many diagonals does the pentagon have?