Willis Thai
MA2212
HW02
1.3-1
A boy found a bicycle lock for which the combination was unknown. The correct combination
is a four-digit number,
d
1
d
2
d
3
d
4
, where
d
i
,
I
– 1, 2, 3, 4, is selected from 1, 2, 3, 4, 5, 6, 7, 8. How
many different lock combinations are possible with such a lock?
8
4
= 4096
1.3-5
How many four-letter code words are possible using the letters in HOPE if:
(a) The letters may not be repeated?
4! = 24
(b) The letters may be repeated?
4
4
= 256
1.3-13 A café lets you order a deli sandwich your way. There are 6 choices for bread, 4 choices for
meat, 4 choices for cheese, and 12 different garnishes (condiments). How many different
sandwich possibilities are there if you choose:
(a) One bread, one meat, and one cheese?
6 x 4 x 4 = 96
(b) One bread, one meat, one cheese, and from 0 to 12 garnishes?
6 x 4 x 4 x 2
12
= 393,216
(c) One bread; 0, 1, or 2 meats; 0, 1, or 2 cheeses; and from 0 to 12 garnishes?
6 x (1 + 4 +
4
C
2
) (1 + 4 +
4
C
2
) x 2
12
= 2,973,696
1.3-15 Among nine presidential candidates at a debate, three are Republicans and six are Democrats.
(a) In how many different ways can the nine candidates be lined up?
9! = 362,880
(b) How many lineups by party are possible if each candidate is labeled either
R
or
D
?
9
C
3
= 84
1.3-19 There are three teams in a cross country race. Team A has 5 runners, team B had 6 runners,
and team C has 7 runners. In how many ways can the runners cross the finish line if we are
only interested in the team for which they run? That is, what is the number of distinguishable
permutations of 5 A’s, 6 B’s, and 7 C’s? (Note that for scoring purposes, only the scores of the
first 5 runners for each team count.)
ଵ଼Ǩ
ହǨǨǨ
= 14,702,688
1.4-1
A common test for AIDS is called the ELISA (Enzyme-Linked Immunosorbent Assay) test.
Among 1,000,000 people who are given the ELISA test, we can expect results similar to those
given in the table.