12.5 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!!)
= $\frac{{n!}}{{(n  r)!\;\;r!}}$

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 5card 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 5card 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,