Math Math Mathy Math

Question 1

What is a permutation?

Answer 1

An order of arrangements of [r] objects without repetition, selected from [n] distinct objects. Where you need to count the # of ways you can arrange items where order is important. ORDER MATTERS!

Question 2

Permutation formula

Answer 2

nPr = n!/(n-r)!

Question 3

Permutations: 7 factorial

Answer 3

7!

Question 4

Permutations: 0!

Answer 4

Always = 1

Question 5

Permutations example: How many ways can 8 cd’s be arranged on a shelf?

Answer 5

[n] = 8 (8 cd's in this problem)
[r] = 8 (arranging all 8 cd's)
nPr = n!/(n-r)!
nPr = 8!/(8-8)!
nPr = 8!/0!
= 8!/1
=8!
=8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
=40320

Question 6

Permutations example: In how many ways can a sorority of 20 members select a president, vp, and treasurer, assuming that the same person cannot hold more than one office?

Answer 6

[n] = 20 (20 members in the sorority)
[r] = 3 (3 offices to be held)
nPr = 20!/(20-3)!
= 20!/17!
= 6840

Question 7

Permutations example: How many different arrangements can be made using 2 of the letters of the word TEXAS, if no letter is to be used twice?

Answer 7

[n] = 5 (5 letters in TEXAS)
[r] = 2 (2 letters at a time)
nPr = 5!/(5-2)!
= 5!/3!
= 20

Question 8

What are combinations?

Answer 8

When you need to count the # of groupings, without regard to order.
Arrangement of [r] objects, without regard to order and without repetition, selected from [n] distinct objects.

Question 9

Combinations formula

Answer 9

nCr = n!/(n-r)! r!

Question 10

Combinations example: In a conference of 9 schools, how many intraconference football games are played during the season if the teams all play each other exactly once?

Answer 10

[n] = 9 (9 teams in conference)
[r] = 2 (2 teams play per game)
nCr = 9!/(9-2)! 2!
= 9!/7! 2!
= 36

Question 11

Combinations example: You are going to draw 4 CARDS from a standard deck of 52 cards. How many different 4 card hands are possible?

Answer 11

[n] = 52 (52 cards in the deck)
[r] = 4 (we want 4 hands) 
nCr - 52!/(52-4)! 4!
= 52!/48! 4!
= 270725

Question 12

Combinations example: 3 marbles are drawn at random from a bag with 3 red and 5 white marbles. How many different draws are there?

Answer 12

[n] = 8 (8marbles in the bag)
[r] = 3 (3marbles are drawn at a time)
nCr = 8!/(8-3)! 3!
= 8!/5! 3!
= 56

Question 13

What is probability?

Answer 13

Used to find out chances, research, and advertising

Question 14

Probability: experiment definition

Answer 14

An act for which the outcome is uncertain (rolling a die, tossing a coin)

Question 15

Probability: sample space definition

Answer 15

[S] set of all possible outcomes of the experiment such that each outcome corresponds to exactly one element in [S]. Elements of [S] are called sample points. If there is a finite # of sample points, that # is denoted [n(S)]

Question 16

Probability: sample space example

Answer 16

Rolling a die would be: S = {1, 2, 3, 4, 5, 6}
Tossing a coin: S = {heads, tails}
Surveying favorite soft drinks: S = {sprite, coke, dr.p}

Question 17

Probability: event definition

Answer 17

Subset [E] of a sample space experiment

Question 18

Probability: event example

Answer 18

Rolling a single die: an event [E] could be rolling an even # is E = {2, 4, 6}
Tossing a coin: an event [E] could be tossing a tails is E = {tails}

Question 19

Empirical Probability

Answer 19

Based on direct observations or experiences, represents the probability that an event E will occur

Question 20

Empirical probability formula

Answer 20

P(E) = # of times x event occurs / total # of observed occurrences = probability that an event E will occur

Question 21

Probability example: The table below lists the results of a student survey pertaining to favorite ethnic foods.  Each student chose only one type of ethnic food for the survey.
Italian: 15
Chinese: 20
Japanese: 3
Thai: 4
Mexican: 30
Other: 10
What is the probability that the student's favorite ethnic food chinese?

Answer 21

n(E) = n(students whose favorite ethnic food is chinese)
n(S) = n(students surveyed) 

n(E) = 20 (20 students liked chinese food best) 
n(S) = 82 (82 total students surveyed)
= 20/82
= 10/41
= 2.44

Question 22

Mean

Answer 22

The average

Question 23

Median

Answer 23

The middle # after they have been put into numerical order

Question 24

Mode

Answer 24

that occurs most often on the list

Question 25

Range

Answer 25

Difference between largest and smallest #s

Question 26

Standard Deviation formula

Answer 26

> Find the average of # set
Subtract each number in the set from the average
Square each of those numbers
Average the set of squared numbers (= variance)
Find square root of variance (= standard deviation)