14.5 Combinations

Combinations

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!

Lessons

Notes:
? combination: nCr = number of selections of r items taken from a set of n distinct items (order does NOT matter!!)
= n!(nr)!r!\frac{{n!}}{{(n - r)!\;\;r!}}
    • a)
      How many ways can a president, a vice president, and a treasurer be selected from a class of 20 students?
    • b)
      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:
    • g)
      flush (5 cards of the same suit)?
  • 3.
    ? problems with "at least", "at most"
    From a standard deck of 52 cards, how many different 5-card hands can be formed containing:
  • 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:
  • 5.
    Five points are marked on a circle. By connecting the points on the circle,
Teacher pug

Combinations

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