1. How many license plates using 6 digits can the state of Vermont issue if repetition of digits is
a. permitted?
b. not permitted?
c. In the 2000 census the population of Vermont was 608,827. Why do you think Vermont allows repetition of digits in its license plates? (It now uses three letters and three numerals.)
2. Most radio stations licensed after 1927 use 4 call letters starting with K or W-for example. WFLA in Tampa or KROW in Huntsville, Missouri. Assuming no repetitions, how many 4-letter sets are possible?
3. In how many different orders can the letters in the set {a, b, c, d} be written?
4. If 6 horses are in a race and they all finish with no ties, in how many ways can the horses finish the race?
5. You may be able to save time if you scan your own purchases at the supermarket Five top reasons (not necessarily in order) people hate this method: Difficult to use. monitored like a criminal, bar scanner does not work, accidental double scan¬ning, mandatory placing of items in the bag. In how many ways can you list these 5 items?
In problems 6-12 compute the given number
6. 8!
7. 9!
8 11!/8!
9. 9!/5!4!
10. P(10,2)
11. P(5,2)/2!
12. 3.P(8,5)
13. A student is taking 5 classes, each of which requires I book. In how many ways can she stack the 5 books she must carry?
14. The Mateland building is a very special building where you can select the qualities for your significant other. The instructions state that you can only visit once. The building is 6 stories tall and the value of the significant other increases as you go higher. You can select a quality for your significant other at any floor or go on to the next floor but you can't go down, except to leave. The floors are labeled with the qualities you desire:
1. Has a job
2. Loves kids
3. Good looking
4. Helps with housework
5. Romantic
a. How many permutations of these 5 qualities can you make?
b. If you decide to build a new 3 story building selecting the floor names from the list of 5. how many different build¬ings are possible?
c. But what happened to the 6th floor? An unsatisfied person, not content with having selected a significant other with the great 5 qualities listed, decided to go up one more floor:
The 6th floor had a sign: You are visitor 7,601,445 and we built this floor to demonstrate how hard it is to please people.
By the way, is 7,601,445 divisiblg by 3? By 5?
15. In how many ways can 3 hearts be drawn from a standard deck of 52 cards?
16. In how many ways can 2 red cards be drawn from a standard deck of 52 cards?
17. How many 3-digit numbers can be formed from the digits 1, 3, 5, 7, and 9 with no repetitions allowed?
18. A red die and a green die are tossed. In how many ways is it possible for both dice to come up even numbers? (Distinguish between the 2 dice.)
19. Out of 5 children, in how many ways can a family have at least 1 boy?
20. If 2 dice are tossed, in how many ways can at least one of the dice come up a 6? (Hint: There are 5 ways a single die can come up not a 6.)
Six coins are tossed; in how many ways can you have
(i) no tails.
(ii) at least 2 heads.
21. How many of the first 100 natural numbers are multiples of 2 or multiples of 5?