# Combinations

##### Examples
###### Lessons
1. Compare the difference between the following 2 scenarios:
1. How many ways can a president, a vice president, and a treasurer be selected from a class of 20 students?
2. How many different committees of 3 people can be selected from a class of 20 students?
2. 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:
1. any 5 cards (no restrictions)?
2. all black cards?
3. 1 black card and 4 red cards?
4. all face cards?
5. 3 Jacks and 2 Kings?
6. 3 Jacks?
3. Problems with "at least", "at most"
From a standard deck of 52 cards, how many different 5-card hands can be formed containing:
1. exactly 2 Diamonds?
2. at least 2 Diamonds?
3. at most 2 Diamonds?
4. 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:
1. at least 3 boys?
2. at most 1 girl?
3. at least 1 girl?
4. at least 2 boys and 2 girls?
5. Five points are marked on a circle. By connecting the points on the circle,
1. How many triangles can be formed?
2. How many line segments can be formed
3. Form a pentagon inside the circle by connecting the 5 points. How many diagonals does the pentagon have?