Fundamental Counting Principle
The word emphasized by Mr. Zeif so you know to use the FCP.
AND
What is 7!
5040
How many ways can you choose 2 marbles from a bag of 7 different marbles if you do not put the first marble back?
42
How many ways can you make a starting basketball line-up of 5 players from a team of 12 players?
792
Making 3-letter words using the letters REGINA: permutation or combination?
Permutation, the order of the letters in a word matters
You are going back-to-school shopping. You can choose from 3 binders, 4 highlighters, and 3 colour pens. How many ways can you get one of each?
36
How many ways can you arrange 5 people in a row?
120
How many 4-digit codes can be made using the digits 1-7, no repetition
840
How many ways can you choose a dance team of 2 ballet dancers and 3 hip-hop dancers from a group of 8 ballet dancers and 7 hip-hop dancers?
28x35 = 980
True or false: order matters when solving a combination counting problem
False, order only matters for permutations
A deli offers 6 sandwiches, 6 drinks, and 4 desserts. How many different combinations can you make if you choose one from each category?
144
What is 8!/5!
336
How many ways can you arrange the letters in WINNIPEG?
10 080
A shepherd is asked to choose his 3 favourite sheep to compete in a sheep beauty pageant. How many ways can he choose them from his flock of 10?
120
How many ways can you go from your house to school if you have to travel 5 blocks north and 3 blocks east?
56
You have 6 ways to go from your house to downtown and 4 ways to go from downtown to work. How many ways can you go from your house to work if you must stop downtown?
24
What is 8!/(2!3!)
3360
A password is 3 letters followed by 3 digits. How many possible passwords have the order consonant, vowel, consonant, even, odd, even? Repetition is possible.
21x5x21x5x5x5 = 275 625
How many ways can we make a 5-card hand with 4 of a kind (4 of one number and 1 of another number)?
For example, JJJJ5 is 4 of a kind
13C1 x 4C4 x 12C1 x 4C1
= 13 x 1 x 12 x 4 = 624
How many ways can we deal 5 diamonds from just the diamonds in a standard deck of cards?
13C5 = 1287
A building has 10 doors. How many ways can you enter and exit the building if you cannot exit from the same door you entered?
90
Solve for n: (n-2)!/(n-3)! = 7
n=9
Solve for n: nP2 = 30
n=6
Student council has 4 boys and 5 girls. A group of 4 is being chosen to attend a field trip. How many different groups have at least 2 girls going?
4C2 x 5C2 + 4C1 x 5C3 + 4C0 x 5C4
= 60 + 40 + 5 = 105
Solve for n: nC2 = 21
n = 7