permutations, combinations
there are 14 different toppings to choose for a pizza. how many ways can michelle choose 6 of them?
14 C 6 = 3003
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
if you can pick 5 different shoes, and 3 different socks, how many ways can you pick them?
5 x 3 = 15
8!
40320
sophia has 5 dishes to wash. how many ways can she arrange the order in which she does them?
5 P 5 = 120
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
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
4!+5!
144
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
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
Ms.sam gives 6 different homework worksheets and 3 different deltamaths, how many different ways can you finish one of each?
10!-6!
3628080
how many ways are there to choose 5 books from a library of 46 books?
46 C 5 = 1370754
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
CFA offers 100 appetizers and 14 foods in how many ways can a person order a two course meal?
100 x 14 = 1400
10!/5!
30240
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
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
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
(7!-3!)+4!
5058