1. 24 1.Bob, Mike, Jim, and Steve are going to the movies. How many different ways can they sit in seats A, B, C, and D below? 2. Coach Hill is picking a captain and co- captain from his 15 players. How many possibilities does he have if they are all equally likely? ABCD 210

2. 1)a) 24 b) 122) a) 6 b) 6 3) a) 120 b) 20 4) the number of permutations of 14 objects taken 3 at a time 5) the number of permutations of 24 objects taken 10 at a time 6) the number of permutations of 30 objects taken 20 at a time 25) 720 26) 5040 27) b) 24 c) Say you are messenger A. There are 6 permutations in the list in part a in which A is first. There are 24 total permutations, so the probability that you are assigned the first delivery is 6/24 = ¼. 28) 1/720

3. Combinations A selection of objects in which order is not important. Example – 8 people pair up to do an assignment. How many different pairs are there?

4. Combinations ABACADAEAFAGAH BABCBDBEBFBGBH CACBCDCECFCGCH DADBDCDEDFDGDH EAEBECEDEFEGEH FAFBFCFDFEFGFH GAGBGCGDGEGFGH HAHBHCHDHEHFHG

5. The number of r-combinations of a set with n elements, where n is a positive integer and r is an integer with 0 <= r <= n, i.e. the number of combinations of r objects from n unlike objects is Combinations

6. Example 1 How many different ways are there to select two class representatives from a class of 20 students?

7. Solution The answer is given by the number of 2-combinations of a set with 20 elements. The number of such combinations is

8. Example 2 From your class of 24, the teacher is randomly selecting 3 to help Mr. Shaw with a project. How many combinations are possible?

9. Your turn! For your school pictures, you can choose 4 backgrounds from a list of 10. How many combinations of backgrounds are possible?

10. Your turn! Coach Hill randomly selects 3 people out of his class of 20 to go to the courts and help him get ready for a tennis match. How many possibilities of people does he have?

11. ORDER MATTERS! Permutations or Combinations Placement Examples: assigned seats, winning a race or running a race, 1 st place, 2 nd place, etc Positions Examples: Pres., Vice Pres, Sec, Tres. Specific job/chore Examples: Hand out markers, pass out papers, etc