Math Problem Statement

A computer store offers a basic desktop computer in a choice of FOUR processor speeds, THREE sizes of read-only memory(ROM), FIVE sizes of fixed disk, and THREE monitor designs.

Each desktop computer should have a processor, a read-only memory, a disk and a monitor.

In how many different ways can a person select a computer from this store ?

Solution

To find the total number of different ways a person can select a desktop computer, we need to consider each component (processor, ROM, disk, and monitor) and the number of choices available for each.

  • Processor speeds: 4 choices
  • ROM sizes: 3 choices
  • Fixed disk sizes: 5 choices
  • Monitor designs: 3 choices

To find the total number of combinations, multiply the number of choices for each component:

4×3×5×3=1804 \times 3 \times 5 \times 3 = 180

Thus, a person can select a computer in 180 different ways.

Would you like any further explanation or details? Here are a few related questions for your exploration:

  1. How would the number of possible combinations change if the store added one more choice for each component?
  2. If the store decided to exclude one of the monitor designs, how would that affect the total number of choices?
  3. What if the store decided to offer 2 types of RAM (e.g., RAM and ROM) instead of just ROM? How would that change the total number?
  4. How would the situation change if the customer had to choose exactly one of the components as a pre-selected default (e.g., pre-installed monitor)?
  5. If the store decided to give a discount for certain combinations of components, how could you calculate the new total number of combinations eligible for the discount?

Tip: When dealing with combinations like this, the principle of multiplication (where the total number of outcomes is the product of the choices for each independent event) is a powerful tool!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Combinatorics
Multiplication Principle

Formulas

Total combinations = (choices for processor) × (choices for ROM) × (choices for disk) × (choices for monitor)

Theorems

Multiplication Principle

Suitable Grade Level

Grades 6-8