Question

There are 3 candidate for a Mathematics, 5 for chemistry and 4 for a Physics scholarship. In how many ways can the scholarship be awarded.

• A. 12
• B. 60
• C. 20
• D. none of these

Hint:

When events are independent and you need them all to occur ("AND" condition), multiply their respective possibilities. If it were a choice of awarding only ONE scholarship in total ("OR" condition), you would add them (\(3+5+4=12\)).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to find the total number of ways to award scholarships. Based on the options, the question implies awarding one scholarship for each of the three distinct subjects (Mathematics, Chemistry, and Physics).


Step 2: Key Formula or Approach:
We use the Fundamental Principle of Counting (Multiplication Rule). If one event can occur in \(m\) ways and a second independent event can occur in \(n\) ways, then the two events can occur together in \(m \times n\) ways.


Step 3: Detailed Explanation:
Number of ways to award the Mathematics scholarship = 3 (since there are 3 candidates)
Number of ways to award the Chemistry scholarship = 5 (since there are 5 candidates)
Number of ways to award the Physics scholarship = 4 (since there are 4 candidates)
Since the selections for each subject are independent of one another, the total number of ways to award all three scholarships is the product of the individual choices: \[ \text{Total ways} = 3 \times 5 \times 4 \] \[ \text{Total ways} = 60 \]

Step 4: Final Answer:
The scholarships can be awarded in 60 ways.