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List the Rule method for the sample size of one red dice and one green dice.
S = {x,y} | 1 <= x <= 6; 1 <= y <= 6}
U = {1, 2, 3, 4, 5, 6}
A = {1, 2, 3}
B = {3, 4, 5}
What is(A ∩ B)?
{3, 4}
U = {1, 2, 3, 4, 5, 6}
A = {1, 2, 3, 4}
B = {3, 4, 5, 6}
What is (A ∩ B)’?
{1, 2, 4, 5, 6}
U = {1, 2, 3, 4, 5, 6}
A = {1, 2, 3}
B = {4, 5}
What is A ∪ B?
{1, 2, 3, 4, 5}
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 3}
B = {4, 5}
What is (A ∪ B)’?
{6, 7, 8, 9}
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 3}
B = {4, 5}
C = {2, 4, 6}
What is (A ∩ C) ∪ B?
{2, 4, 5}
2: 21: Registrants at a large convention are offered 6 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?
18
2.22: In a medical study, patients are classified in 8 ways according to whether they have blood type AB AB−, A+, A−, B+, B−, O+, or O−, and also accord- ing to whether their blood pressure is low, normal, or high. Find the number of ways in which a patient can be classified.
24
Combinations
Order does not matter
Combinations rule:
n
C
r
n!/r!(n-r)!
A California study concluded that following 7 simple health rules can extend a man’s life by 11 years on the average and a woman’s life by 7 years. These 7 rules are as follows: no smoking, get regular exer- cise, use alcohol only in moderation, get 7 to 8 hours of sleep, maintain proper weight, eat breakfast, and do not eat between meals. In how many ways can a person adopt 5 of these rules to follow
(a) if the person presently violates all 7 rules?
Hint: Combination formula
21
A California study concluded that following 7 simple health rules can extend a man’s life by 11 years on the average and a woman’s life by 7 years. These 7 rules are as follows: no smoking, get regular exer- cise, use alcohol only in moderation, get 7 to 8 hours of sleep, maintain proper weight, eat breakfast, and do not eat between meals. In how many ways can a person adopt 5 of these rules to follow
(b) if the person never drinks and always eats breakfast?
Hint: Combination formula
10
2.30: In how many different ways can a true-false test consisting of 9 questions be answered?
512
2.31: A witness to a hit-and-run accident told the po- lice that the license number contained the letters RLH followed by 3 digits, the first of which was a 5. If the witness cannot recall the last 2 digits, but is cer- tain that all 3 digits are different, find the maximum number of automobile registrations that the police may have to check.
72
3.42:
(a) How many distinct permutations can be made from the letters of the word COLUMNS?
(b) How many of these permutations start with the letter M?
a. 5040
b. 720
3.32:
(a) In how many ways can 6 people be lined up to get on a bus?
(b) If 3 specific persons, among 6, insist on following each other, how many ways are possible?
(c) If 2 specific persons, among 6, refuse to follow each other, how many ways are possible?
a. 720
b. 144
c. 480
2.38: Four married couples have bought 8 seats in the same row for a concert. In how many different ways can they be seated
(a) with no restrictions?
(b) if each couple is to sit together?
(c) if all the men sit together to the right of all the women?
a. 40,420
b. 384
c. 576
Circular permutation formula
(n-1)!
In how many ways can 3 oaks, 4 pines, and 2 maples be arranged along a property line if one does not distinguish among trees of the same kind?
Hint: Multinomial Law
1260
2.55: If each coded item in a catalog begins with 3 distinct letters followed by 4 distinct nonzero digits, find the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even.
20/234
