## 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:

 Flavors Cones 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?

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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