Fundamental Counting Principle

Factorials

Permutations

Combinations

Permutations or Combinations

100

What special word tells you to use the FCP?

AND

100

What is 7!

5040

100

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

100

How many ways can you make a starting basketball line-up of 5 players from a team of 12 players?

792

100

Making 3-letter words using the letters REGINA: permutation or combination?

Permutation, the order of the letters in a word matters

200

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

200

How many ways can you arrange 5 people in a row?

120

200

How many 4-digit codes can be made using the digits 1-7, no repetition

840

200

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

200

True or false: order matters when solving a combination counting problem

False, order only matters for permutations

300

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

300

What is 8!/5!

336

300

How many ways can you arrange the letters in WINNIPEG?

10 080

300

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

300

How many ways can you go from your house to school if you have to travel 5 blocks north and 3 blocks east?

56

400

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

400

What is 8!/(2!3!)

3360

400

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

400

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

_{13}C_{1 }x _{4}C_{4 }x _{12}C_{1 }x _{4}C_{1}

= 13 x 1 x 12 x 4 = 624

400

How many ways can we deal 5 diamonds from just the diamonds in a standard deck of cards?

_{13}C_{5} = 1287

500

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

500

Solve for n: (n-2)!/(n-3)! = 7

n=9

500

Solve for n: _{n}P_{2 }= 30

n=6

500

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?

_{4}C_{2 }x _{5}C_{2 }+ _{4}C_{1} x _{5}C_{3} + _{4}C_{0 }x _{5}C_{4}

= 60 + 40 + 5 = 105

500

Solve for n: _{n}C_{2} = 21

n = 7

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