Discrete mathematical methods of computing Counting and Probability Excercises S

Question

Discrete mathematical methods of computing

Counting and Probability Excercises

Solve the following;

1. A catered menu is to include a soup, a main course, a dessert, and a beverage. Suppose a customer can select from four soups, five main courses, three desserts, and two beverages. How many different menus can be selected?

2. Find the number of different permutations of the letters in the word GROUP.

3. Find the number of distinguishable permutations of the letters in ASSOCIATIVE.

4. At a certain college, the housing office has decided to appoint, for each floor, one male and one female residential advisor. How many different pairs of advisors can be selected for a seven-story building from 12 male candidates and 15 female candidates?

5. In how many ways can five balls be chosen so that

(a)all five are red?

(b)all five are black?

6. (a)The sum of the numbers is less than 7.

(b)The sum of the numbers is greater than 8.

7. (a)What is the probability of correctly guessing a person’s four-digit PIN?

(b)People often use the four digits of their birthday (MM-DD) to create a PIN. What is the probability of correctly guessing a PIN created this way, if the birthday is known?

Explanation / Answer

1.   A catered menu is to include a soup, a main course, a dessert, and a beverage. Suppose a customer can select from four soups, five main courses, three desserts, and two beverages. How many different menus can be selected?

A.   He can select the menu in the following different ways

4(soups)*5(main courses) *3(deserts)*2(beverages) = 120 ways

2.   Find the number of different permutations of the letters in the word GROUP.

A.   As the are no repetitions hence number of permutations of the given word is

5! =120 ways

3.   Find the number of distinguishable permutations of the letters in ASSOCIATIVE.

A.   The given word has 2S’s,2A’s,2I’s hence the total number of ways are

11! / (2!*2!*2!)

=4989600 ways

4.   At a certain college, the housing office has decided to appoint, for each floor, one male and one female residential advisor. How many different pairs of advisors can be selected for a seven-story building from 12 male candidates and 15 female candidates?

A.   7 out of 12 males need to be selected and to be paired with 7 out of 15 females.

Hence, C(12,7)*C(15,7) = 729*6435=4691115

5. In how many ways can five balls be chosen so that

(a)all five are red?

(b)all five are black?

Incomplete question

6. (a)The sum of the numbers is less than 7.

(b)The sum of the numbers is greater than 8.

Incomplete question

7. (a)What is the probability of correctly guessing a person’s four-digit PIN?

A.Total number of ways to get a person’s 4 digit pin is 10*10*10*10 = 10000

Prob in the first try is 1/1000

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.