Permutations or Combinations
Choosing 7 people for a job from 100 applicants?
Combination
Solve: How many ways can you pick the President, Vice President, Treasurer, and Media Sponsor from a group of 4 people?
4P4 = 4! =4*3*2*1 = 24
Solve: How many different way can you pick 4 toppings from a list of 10? (no repetition allowed.)
10C4 = (10!)/4!(10-4)! = (10!)/(4!)(6!)= 210
For P(AlB) what does l stand for?
Given
How many pages were there in the notes?
16
How many different ways can you arrange the letters in RACECAR?
Permutation
Solve: How many ways can you make a 4 digit passcode using the numbers 0-9?
10P4 = 104 = 10,000
Solve: How many different ways can you pick 8 people from a class of 20?
20C8 =(20!)/8!(20-8)! = (20!)/(8!)(12!) = 125,970
For P(AlB) does P(A) or P(B) go on the bottom?
P(B)
What is the difference between nPr and nCr?
One is used for probability and one is used for combination.
In addition state whether you can repeat or not.
Ways to arrange the 4 numbers on a combination lock.
Permutation and you can repeat
Solve: How many ways can you arrange the letters in MISSISSIPPI if you only use 5 letters?
11P5 = (11!)/(11-5)! = 55,440
Solve: How many ways can you pick 4 captains from a class of 20 people?
20C4= (20!)/4!(20-4)! = (20!)/(4!)(16!) = 4,845
For P(AlB) what goes on top?
P(AnB)
What is the difference between Combination and Probability?
Probability - order does matter
Combination - order does not matter
In addition state whether you can repeat or not.
Drawing winning tickets for a raffle at a car show.
Combination and you cannot repeat.
Solve: How many different ways can you make a license plate with the first 3 characters being letters and the last 3 characters being digits? (you can repeat)
26P3*10P3=263*103=17,576,000
Solve: How many ways can you pick 3 toppings from a list of 15 if you can repeat?
15C3 = (3+15-1)!/3!(15-1)! = 17!/3!14!= 680
If A = # of students older than 15 and B = # of students that drive. What does P(BlA) stand for?
The probability that a student drives, given that they are older than 15.
When can you type both nPr and nCr in the calculator?
When your event does not repeat.
Give me an example of something that is a permutation where you cannot repeat.
Answers may vary. (ex: picking the 1st, 2nd, and 3rd place winners)
Solve: How many different ways can you make a license plate with the first 3 characters being letters and the last 3 characters being digits? (you cannot repeat)
26P3*10P3=[26!/(26-3)!][10!/(10-3)!] = 11,232,000
Solve: How many different lottery combinations can you make from 30 numbers if you choose 4 and place the ball back each time?
30C4 = (4+30-1)!/4!(30-1)! = 33!/4!29!=40,920
There are 150 students in the foreign language course. 70 take Spanish, 80 take Japanese, and 30 take Spanish and Japanese. What is that chance that you pick a student who has Spanish, given that they take Japanese already.
P(Spanish l Japanese) = P(Spanish and Japanese) /P(Japanese) = 30/80 = 3/8 = 0.375
How do you type 10C3 in the calculator? (One member must go up to Mrs. Bain and show her)
one example:
10 -> MATH -> PRB -> nCr -> 3 -> ENTER