probability

permutations, combinations

100

there are 14 different toppings to choose for a pizza. how many ways can michelle choose 6 of them?

14 C 6 = 3003

200

sophia has 5 dishes to wash. how many ways can she arrange the order in which she does them?

5 P 5 = 120

300

ms. sam has 16 students in her geometry class. she has 4 prizes to give away, stickers, erasers, paper clips, and pencils. how many ways can she choose 4 students to win 

16 P 4 = 43680

400

how many ways are there to choose 5 books from a library of 46 books?

46 C 5 = 1370754

500

ms. sam is choosing a new six-character password for her deltamath account. the password can include any letters and any digits, but can't repeat characters. how many passwords could be possible?

36 P 6 = 1402410240

distribution

100

X     |   P(X)

--------------

20       0.37

200      0.15 

2000    0.23

IS THIS PROBABILITY DISTRIBUTION VALID? (yes/no, why/why not)

no, b/c the decimals don't add to 1, they add to 0.75

200

X     |   P(X)

--------------

0       0.50

1       0.25 

2       0.10

3       0.15

IS THIS PROBABILITY DISTRIBUTION VALID? (yes/no, why/why not)

yes, b/c the decimals add to 1

300

X     |   P(X)

--------------

40       0.19

45       0.13

50       0.24

55       0.17

60       0.34

IS THIS PROBABILITY DISTRIBUTION VALID? (yes/no, why/why not)

no, b/c the sum of of the decimals is over 1

400

X     |   P(X)

--------------

2       0.50

8       0.25 

14     0.25

IS THIS PROBABILITY DISTRIBUTION VALID? (yes/no, why/why not)

yes, b/c the decimals add to 1

500

X     |   P(X)

--------------

23       0.20

34       0.20 

45       0.25

56       0.20

67       0.15

IS THIS PROBABILITY DISTRIBUTION VALID? (yes/no, why/why not)

yes, the sum of the decimals equals 1

counting principle

100

if you can pick 5 different shoes, and 3 different socks, how many ways can you pick them?

5 x 3 = 15

200

A restaurant has 5 appetizers, 8 beverages, 9 entrees, and 6 desserts on the menu how many different ways can you chose one of each?

5 x 8 x 9 x 6= 2160

300

Ms.sam gives 6 different homework worksheets and 3 different deltamaths, how many different ways can you finish one of each?

6 x 3 = 18

400

CFA offers 100 appetizers and 14 foods in how many ways can a person order a two course meal?

100 x 14 = 1400

500

at a banquet there are 3 entree choices 4 salad choices and 6 dessert choices how many possible dinners could be created?

3 x 4 x 6= 72

factorials

100

8!

40320

200

4!+5!

144

300

10!-6!

3628080

400

10!/5!

30240

500

(7!-3!)+4!

5058