Transcript 5-10 6th grade math

11-6
6th grade math
Permutations and Combinations
Objective
• To count the number of ways to choose things
when order does and does not matter
• Why? To know how to count arrangements
when order matters (permutations)and when
order does not matter (combinations).
California State Standards
SDP 3.1 : Represent all possible outcomes of
compound events in an organized way (e.g., …
grids, tree diagram) …
MR 2.4: Use a variety of methods, such as words,
numbers, symbols, charts, graphs, tables,
diagrams, and models, to explain mathematical
reasoning.
• Permutation
Vocabulary
– Each possible arrangement of the outcomes of an event where
order is important. Will be a bigger number than a combination.
• To solve: multiply using factorial product of how many ways. The answer
is the number of possibilities. The factorial product = x!
– Who will be president and who will be treasurer
» 23 students; (23 students, – 1 other student = 22)
» 23 x 22 = 506 permutations
To remember is permutation: Think of a perm in your hair. Ordering the way the hairdresser puts a perm in your hair is very
important.
Combination
– Each possible arrangement of the outcomes of an event where
order is not important. Will be a smaller number than a
permutation.
• To solve: permutation ÷ number in the combo
» Two people wanting to be president/treasurer
» 506/2 = 253 combinations
• Ways to choose a class treasurer after president is chosen
Think of the ways you can comb your hair. The order in which your comb your hair really does not matter.
How to Solve Permutations
1) Read problem. Be sure
order does matter
(permutation).
2) Multiply the factorial
product by number of
arrangements needed.
3) Multiply carefully
Put 2 different-colored balloons
on display. 5 Colors: red, blue,
yellow, green, orange. How
many different arrangements?
Order matters, don’t repeat same
2 colors.
5! by 2 spaces
5x4
= 20 different arrangements
How to Solve Combinations
1) Read problem. Be sure
order does NOT matter (=
combination).
2) Divide the permutation by
the number in the combo
3) Divide carefully
Find the number of
arrangements to make if
put in 2 different colored
balloons and order of
arrangement does not
matter.
Permutation =
5 x 4 = 20
# in combo = 2 colors
20/2 = 10 choices or
arrangements
Try It!
#1 & 2) Decide whether or not order
matters in each situation.
1) Choosing 5 CD’s from a list
of 20
2) Choosing 5 digits for a
password
3) How many 3-letter
permutations can be made
from the letters GREAT?
4) 4 kinds of fruit. Put 3 kinds
in a basket. How many
specific arrangements
(permutations)?
1) Order not matter
2) Order does matter
3) 5! By 3 spaces
=5x4x3
= 60 permutations
4) 4! By 3 spaces
=4x3x2
= 24 arrangements
Objective Review
• To count the number of
ways to choose things
when order does and
does not matter
• Why? You now know how to
count arrangements when order
matters (permutations)and when
order does not matter
(combinations).
Independent Practice
• Complete problems 511
• Copy original problem
first.
• Show all work!
• If time, complete Mixed
Review: 12-15
• If still more time, work
on Accelerated Math.