1. Combinations
Lesson 10.2A

2. ACT Practice
In a recent survey, 14 people found their mayor to be “very competent”. This number is exactly 20% of the people surveyed. How many people were surveyed?
ii) If x²=50, then which of the following could be true?
-8 < x < -7 b) -7 < x < -6
c) 5 < x < 6 d) 25 < x < 26
e) 50 < x < 51

3. Warm-ups
Simplify
In how many ways can the 4 remaining Republican candidates line up on stage for tonight’s debate?
c) The new basketball warm-ups come in S, M, or L, red or black, half-zip or full zip. You can have the JM logo embroidered on the sleeve if you like. How many possibilities are there?

4. d) Evaluate 5P3. Show your work
d) Evaluate 5P3. Show your work. e) If ten teams were competing in the final round of the Olympic bobsled competition, in how many ways could they earn gold, silver, and bronze medals?

5. With your partner Try to find the answer in two different ways
5 friends want a ride home
You have your tuba in the backseat and can only fit two in the car.
How many different groups
of two are possible?

6. Combinations
When selecting r different objects from a group of n, the selection can be made in
nCr = ways.
A combination implies that you are merely selecting a group. The order is not relevant. There are not distinguishable jobs, roles, or tasks.

7. Beyonce’ 3 extra tickets, 6 good friends
How many different groups of three friends could you choose?

8. Art School Application
You have a portfolio of 12 pieces of artwork. You plan to submit 4 for an art school application. In how many ways can you choose the 4 pieces to submit?
495

9. 5 dollar footlong challenge
a) How many different sub sandwiches can be ordered with 3 toppings if we may choose from lettuce, spinach, tomatoes, onions, cheese, pickles, cucumbers, peppers, and olives? 84
b) What if I said with 2 OR 3 toppings?
= 120
c) What if you could also choose from 6 types of bread?
120x6 = 720

10. Cards

11. How many different five card hands contain
5 face cards?
4 queens and 1 other card?
5 clubs or 5 spades?
Answers:
a) 792 b) 1x48 = 48 c) = 2574

12. Combination or Permutation?
5 teachers out of 60 to be dance chaperones
2 toppings out of 10 to make a pizza
40 songs out of 100 for playlist for the dance
4 students out of 115 NHS members to be president, vice-president, secretary, and treasurer
3 fruits out of 15 to make a fruit salad
9 baseball players out of 20 to make starting line-up