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Combinations

Practice Problems



If you need some more help, you may want to review the Combination section again.

Problems With Solutions

1. At Louie's Licks, the following ice cream flavors and cones are offered:

ice cream!Flavorsice cream! ice cream!Conesice cream!
Chocolate Waffle
Vanilla Sugar
Mint Chocolate Chip Cake
Strawberry
Rocky Road


For $1.50, a customer may get "Louie's Delight" - the cone of his or her choice and with two different scoops of ice cream. How many different ways may a person order "Louie's Delight" ?

For $2.50, a customer may get "Monster Madness" - the cone of his or her choice with 3 scoops of ice cream. With this special, one may order the same ice cream more than once. How many different ways can a person order "Monster Madness"?

2. Mr. Pascal must select an ice hockey team of 9 players from 17 seniors and 15 juniors. How many ways may he select a team if...
  1. he has no restrictions?
  2. two seniors, Anthony and Marc-Eric are the best goalies and must be on the team?
  3. he must pick 5 seniors and 4 juniors?


3. Shui is taking her biology quiz, and is instructed to answer 7 out of the 10 questions. How many different ways may she answer the questions if...
  1. she has no restrictions?
  2. she must answer 4 out of the first 5, and 3 out of the last 5?
  3. she must answer at least 3 of the first 5?


4. The English alphabet has 26 letters - five of those are vowels, the others are consonants. For this question, consider a "word" to have no two letters which are the same - thus "funny" would not be a "word" since it has two n's.

  1. How many 5 letter "words" are there?
  2. What is the number of 10 letter "words" that have 4 or more vowels?
  3. How many 7 letter "words" start with 'x' and have either an 'e' or an 'i' in them?


5. Jacie is playing a game of poker, where she is dealt 5 cards from the usual deck of 52. How many ways may she be dealt (a) four of a kind? (b) a pair of jacks?


On Your Own



1. Damien selects six cards from a standard deck. How many ways may he choose...
  1. six hearts? [Solution]
  2. three hearts and three spades? [Solution]
  3. six spades or six clubs? [Solution]


2. The majority leader of the U. S. Senate must select 9 members of the 100 in the Senate for a committee on agriculture. Unfortunately, Senator Kennedy and Senator Helms will get into a fight if they are both on the same committee. How many different committees may the majority leader select if Kennedy and Helms cannot both be on the same committee? [Solution]

3. How many ways can you select 2 clubs or 2 face cards from a standard deck? [Solution]

4. An urn contains 40 ping-pong balls which are labelled #1-#40. Five balls are selected from the urn at random.

  1. How many different selections have #39 or #17? [Solution]
  2. How many selections contain exactly one prime number? [Solution]
  3. How many selections have #7 and no multiples of 5? [Solution]


5. A gambler is dealt 5 cards from an ordinary deck of 52 cards. Determine the different number of ways he may recieve... If you have mastered Combinations, move on to the next section: Probability.






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