Transcript Slide 1 - Fort Bend ISD

Counting Principle part 2
I. Math symbols and formulas for Counting Principles.
A) Basic Counting Principle = m x n where you have m things and n
things and want them arranged every possible way.
B) Combinations (counting principle) where order does NOT matter.
It comes from the Permutations formula.
1) If repeating is NOT allowed
(like a lottery ticket)
2) If repeating IS allowed
(like a combination lock)
n = number of objects in the set
r = how many objects we are selecting/arranging.
! = factorial MENU  5 Probability  1 Factorial
Counting Principle part 2
Examples: Combinations without repeating
1) How many ways can you create a password that uses 5
different lower case letters in a row.
26!
5!26  5!
26!

(5!21! )
 65,780
2) If a lottery ticket has 59 numbers and you have to pick 5 of
them, how many different ways can you fill out a lottery
ticket? This does not include picking the powerball (1
number out of 36).
59!
5!59  5!

59!
(5!54! )
 5,006,386
Counting Principle part 2
C) If the objects are NOT allowed to be repeated, then
you can use a button on the calculator to find how many
combinations (counting principle) there are. ( nCr )
1) MENU  5 Probability  3 Combinations nCr(n,r)
n = number of objects
r = how many are being selected.
Examples:
1b) A 5 letter lower case password (no repeating).
n = 26 & r = 5 type MENU53 type 26,5 in the ( )
Screen shows nCr(26,5) the answer is 65780.
2b) A 59 number lottery ticket, pick 5 numbers.
n = 59 & r = 5
nCr(59,5) = 5,006,386
Counting Principle part 2
Examples: Combinations with repeating.
3) How many ways can you create a password that uses any 5
lower case letters? (repeating is allowed)
30!
(26  5  1)!

(5!25! )
5!(26  1)!
 142,506
Note: There is NOT a button to do repeating combinations. You
have to use the formula.