Consider a group of n distinct individuals or objects. An umordered subset of the group is called a combination. The number of combination of size k that can be formed from n distinct objects is denoted by Ck,n or Ck,n n! (2) = k! (n - k)! 2. Consider ordering ramen. Assume there are seven choices of additional toppings: Mushrooms (MU), Menma (ME), Green Onion (G), Corn (C), Egg (E), Nori (N), Fried Garlic (F). N=7 a. How many ways are there to choose 3 additional toppings? N=6 7! C 2₁2 = (3) 31 (2-3) 17 71 7.6.5 43.27 31(7-3)) 3! (4)! 321 (4.3.2.1) -765-35 b. Let A be the event that Nori is not ordered. Assuming each combination is equally likely, what is P(A)? S-{MAU; MENMA, G, C, E, E P(A) 1654321 3!(6-3) 31 (3) 31 (21) = 221321 61 (3,6 = 31 (6-3) = 20 c. Let B be the event that either Menma or Green Onion is ordered, but not both. What is P(B)? (UNION OF 2 EVENTS -INTERSECTON) ==
Consider a group of n distinct individuals or objects. An umordered subset of the group is called a combination. The number of combination of size k that can be formed from n distinct objects is denoted by Ck,n or Ck,n n! (2) = k! (n - k)! 2. Consider ordering ramen. Assume there are seven choices of additional toppings: Mushrooms (MU), Menma (ME), Green Onion (G), Corn (C), Egg (E), Nori (N), Fried Garlic (F). N=7 a. How many ways are there to choose 3 additional toppings? N=6 7! C 2₁2 = (3) 31 (2-3) 17 71 7.6.5 43.27 31(7-3)) 3! (4)! 321 (4.3.2.1) -765-35 b. Let A be the event that Nori is not ordered. Assuming each combination is equally likely, what is P(A)? S-{MAU; MENMA, G, C, E, E P(A) 1654321 3!(6-3) 31 (3) 31 (21) = 221321 61 (3,6 = 31 (6-3) = 20 c. Let B be the event that either Menma or Green Onion is ordered, but not both. What is P(B)? (UNION OF 2 EVENTS -INTERSECTON) ==
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Consider a group of n distinct individuals or objects. An umordered subset of the
group is called a combination. The number of combination of size k that can be
formed from n distinct objects is denoted by Ck,n or
Ck,n
n!
(2) = k! (n - k)!
2. Consider ordering ramen. Assume there are seven choices of additional toppings:
Mushrooms (MU), Menma (ME), Green Onion (G), Corn (C), Egg (E), Nori (N),
Fried Garlic (F).
N=7
a. How many ways are there to choose 3 additional toppings?
N=6
7!
C 2₁2 = (3) 31 (2-3) 17
71 7.6.5 43.27
31(7-3)) 3! (4)! 321 (4.3.2.1)
-765-35
b. Let A be the event that Nori is not ordered. Assuming each combination is
equally likely, what is P(A)? S-{MAU; MENMA, G, C, E, E
P(A)
1654321
3!(6-3) 31 (3)
31 (21) = 221321
61
(3,6 = 31 (6-3)
= 20
c. Let B be the event that either Menma or Green Onion is ordered, but not both.
What is P(B)?
(UNION OF 2 EVENTS -INTERSECTON)
==
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