Registrants at a large convention are offered G sightseeing tours on each of 3 d
ID: 3239587 • Letter: R
Question
Registrants at a large convention are offered G sightseeing tours on each of 3 days. In how many ways can a person arrange to go on a sightseeing tour planned by this convention? b. Nine people are going on a skiing trip in 3 cars that hold 2. 4 and 5 passengers, respectively. In how many ways is it possible to transport the 9 people to the ski lodge, using all cars? c. A developer of a new subdivision offers a prospective home buyer a choice of 4 designs, 3 different heating systems, a garage or carport, and a patio or screened porch. How many different plans are available to this buyer? d. A young boy asks his mother to get five games from his collection of 10 arcade and 5 sports games. How many ways are there that his mother will get 3 arcade and 2 sports games, respectively?Explanation / Answer
Solution:
(b)
NOTE: It is not clear whether Car #1 must always carry at
least 1person. Thus, 2 results are presented below. The
first result allows Car #1 to carry 0 people, in addition to
1 or 2 people. The second requires Car #1 to always carry
at least 1 person.
Car #1 may contain {0, 1, or 2}people, which will
determine the possible distribution of people to
other cars:
Car #1 Car#2 Car#3 #Combinations
(0-2) (0-4) (0-5)
-------- --------- ------- --------------------
0 4 5 C(9,4)*C(5,5) = 126
1 4 4 C(9,1)*C(8,4)*C(4,4) = 630
1 3 5 C(9,1)*C(8,3)*C(5,5) = 504
2 4 3 C(9,2)*C(7,4)*C(3,3) =1260
2 3 4 C(9,2)*C(7,3)*C(4,4) = 1260
2 2 5 C(9,2)*C(7,2)*C(5,5) = 756
---------------------------------------
TOTAL = 4536
SOLUTION:
----> {Total # With All Above Possible} = 4536
----> {Total # Without Car #1 = 0} = 4410 (<--- try this first)