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Problems Involving Fundamental Counting Principle


1. Patrick wants to buy a computer system. In a computer shop, a customer can choose one of the 4 monitors, one of the 2 keyboards, one of the 4 CPU, and one of 3 printers. Determine the number of possible systems that Patrick can choose from.


2. An ice cream parlor is offering different flavors of ice cream with two kinds of containers available, cone and paper cup. The flavors of their ice cream include cheese, vanilla, mango, and chocolate. What is the total number of possible combinations if a customer can choose a container and 3 flavors of ice cream?


3. Emma has 5 blouses, 3 skirts, and 4 pairs of shoes. In how many different ways consisting of a blouse, a skirt, and a pair of shoes can Emma dress up?


4. Tess, Rina, Rose, Ronnie, Bryan, and Gab are all members of the Student Council. In how many ways can you form a committee of three students?



Problems Involving Probability of Simple Events


5. A letter is to be chosen from the letters of the word EXTRAVAGANT. What is the probability that it is a consonant?


6. An auditor of a club is to be selected from 8 Grade 7, 9 Grade 8, 12 Grade 9, and 5 Grade 10 students. What is the probability that he/she is not a Grade 8 student?


7. A spinner is divided into parts and whose colors are similar to a color wheel. What is the probability that the pointer lands on a secondary color?


8. Slips of paper are numbered 4, 5, 6, …, 34, folded into similar squares and placed in a bowl. If a paper is to be picked at random, what is the probability that the number is a prime number?

Respuesta :

MrRoyal

The questions are illustrations of combination and probability

  • Combination involves the ways of choosing or selecting an item from a group of items
  • Probability involves the chance of choosing or selecting an item from a group of items

1. Number of systems to choose from

The given parameters are:

Monitors = 4

Keyboard = 2

CPU = 4

Printer = 3

The number of systems to choose from is:

n = 4 * 2 * 4 * 3 = 96

Hence, Patrick can choose from 96 systems

2. Combination of Ice cream

The given parameters are:

Containers = 2

Flavors = 4

The number of total combination to choose from is:

n = 2 * 4C3 = 8

Hence, the number of total combination is 8

3. Emma dressing up

The given parameters are:

Blouse = 5

Skirt = 3

Shoes = 4 pairc

The number of ways to dress up:

n = 5 * 3 * 4 = 60

Hence, Emma can dress up in 60 ways

4. Members of committee

The given parameters are:

Students = 6

Members of committee = 3

The number of ways to form a committee is:

n = 6C3 = 20

Hence, there are 20 ways to form the committee

5. Probability of consonant

We have:

Letters = 11

Consonnats = 7

The probability of selecting a consonant is:

P = 7/11

P = 0.636

Hence, the probability of selecting a consonant is: 0.636

6. Probability of not selecting a grade 8 student

We have:

Total students = 34

Students not in grade 8 = 25

The probability that a student is not in grade 8 is:

P = 25/34

P = 0.735

Hence, the probability that a student is not in grade 8 is 0.735

7. Probability of a secondary color

Not enough details to solve

8. Probability of a prime number

There are 9 prime numbers in a total number of 31 numbers from 4 to 34.

So, the probability that a number is prime is:

P = 9/31

P = 0.290

Hence, the probability that a number is prime is 0.290

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