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:
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:
- How would the number of possible combinations change if the store added one more choice for each component?
- If the store decided to exclude one of the monitor designs, how would that affect the total number of choices?
- 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?
- 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)?
- 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!
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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
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