Chapter 6&9 Respond to each exercise with a clear and well justified answer. Sho

Question

Chapter 6&9 Respond to each exercise with a clear and well justified answer. Show your work neatly on separate sheets of pa Due May S* per I. Prove or Disprove: For all sets A. B and C. (A-B)-(B-C)= A-B. 2. Prove or Disprove: For all sets A and B. (A -B)U (B -A) AUB. 3. Prove or Disprove: For all sets A and B, (A-B) n (B -A)0. 4. Find each of the following: a how many numbers are there between 100 and 1,000, including 100 and 1,000? b. how many of these numbers (from part a) have three distinct odd digits? c. the probability that when a number from part a is randomly selected it has three distinct odd digits. 5. A large pile of coins consists of pennies, nickels, dimes, and quarters (at least 12 of each). a. How many distinct ways can 12 coins be chosen at random in no particular order? b. How many of these ways (from part a) contain at least one of each type of coin? c. How many of the ways (from part a) consist of exactly 6 pennies? d. What is the probability that 12 coins chosen from the original pile at random in no particular order consist of exactly 6 pennies?

Explanation / Answer

Atleast 12 p , 12 n , 12 d and 12 q

We need
p + n + d + q = 12

Now, number of variables = n = 4
Sum, S= 12

(S + n - 1) C (n - 1)

(12 + 4 - 1) C (4 - 1)

15 C 3

455 --> ANS

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b)
non-zero solutions....

(S - 1) C (n - 1)

(12 - 1) C (4 - 1)

11 C 3

165 ----> ANS

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d)
Exactly 6 pennies :

We have n + d + q = 12 - 6

n + d + q = 6

S = 6
n = 3

So, we have
(s + n -1) C (n - 1)

8 C 2

28 ----> ANS

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