Combinations

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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?