COMBINATIONS

COMBINATIONS

Open Ended

Form another word from the letters of the word COMBINATION

*What is a Permutation?

*How do you solve a Permutation?

*Give an example of a Permutation

COMBINATIONS

It is a selection of possible arrangements of objects without regard to the order in which objects are selected.

EXAMPLE:

Suppose we have a set of 3 letters: A, B, C. In how many ways we can select 2 letters from that set.
AB, AC, BC

The number of combinations n objects taken r at a time is expressed in the follwing ways:
nCr = nPr/r! = n!/(n-r)!r!

C(n,r) = number of combinations
n = number of elements in a set
r = number of elements that can be selected in a set
! = factorial

3 ways to solve a Combinations:
Example: Illustrate all possible combinations in the given set taken 2 at a time.
Leira (L), Justin (J), Ana (A), Max (M), Boy (B)

1. Listing Method

LJ, LM, JA, JB, AB, LA, LB, JM, AM, MB

3 ways to solve a Combinations:
Example: Illustrate all possible combinations in the given set taken 2 at a time.
Leira (L), Justin (J), Ana (A), Max (M), Boy (B)

2. Tree Diagram

3 ways to solve a Combinations:
Example: Illustrate all possible combinations in the given set taken 2 at a time.
Leira (L), Justin (J), Ana (A), Max (M), Boy (B)

3. Formula
n = 5, r = 2
C(n,r) = n!/(n-r)!r!

GROUP ACTIVITY: Solve a combination using a specified way.
FORMULA
Group 1: C(8,3) =
Group 2: C(10,4) =
LISTING
Group 3: Given (M, A, R, Y) taken 2 at a time
Group 4: Given (G, R, A, C, E) taken 3 at a time
TREE DIAGRAM
Group 5: Inn how many ways can a coach choose three runners from a five runner?
Group 6: In how many ways can you select a committee of 2 out of 5 employees?

GROUP ACTIVITY: Solve a combination using a specified way.
FORMULA
Group 1: C(8,3) = 56
Group 2: C(10,4) = 210
LISTING
Group 3: Given (M, A, R, Y) taken 2 at a time = 6
Group 4: Given (G, R, A, C, E) taken 3 at a time = 10
TREE DIAGRAM
Group 5: In how many ways can a coach choose three runners from a five runner? = 10
Group 6: In how many ways can you select a committee of 2 out of 5 employees? = 10

Give examples of a situations that illustrates combinations.

--How do you determine if the situation involves combinations?
--How do you illustrate the combinations of an object?
--What are the 3 ways to solve a combinations?
--What is the most convenient method to use and why?

ASSESSMENT:
Solve using any method and show your solution.
1. Forming 2 digit numbers from 2, 4, 6, 8.
2. Dealing 12 cards from a pack of 52.
3. Choosing a president, a treasurer, and a secretary among 7 candidates.
4. Forming a committee of 6 persons from 10 people.
5. Selecting 3 people from Dane, Dax, Anne, Ardie, and Jade to attend meeting.

ANSWER:
1. Forming 2 digit numbers from 2, 4, 6, 8. = 6
2. Dealing 3 cards from a pack of 52. = 22,100
3. Choosing a president, a treasurer, and a secretary among 7 candidates. = 35
4. Forming a committee of 6 persons from 10 people. = 210
5. Selecting 3 people from Dane, Dax, Anne, Ardie, and Jade to attend meeting. = 10

ASSIGNMENT
1. Give 5 examples of a real life scenario that illustrates a combination.
2. Solve using any three ways.