Question: In how many ways can 3 different colored balls be arranged in a line?
Options:
6
3
9
12
Correct Answer: 6
Solution:
The number of arrangements of 3 different colored balls is 3! = 6.
In how many ways can 3 different colored balls be arranged in a line?
Practice Questions
Q1
In how many ways can 3 different colored balls be arranged in a line?
6
3
9
12
Questions & Step-by-Step Solutions
In how many ways can 3 different colored balls be arranged in a line?
Correct Answer: 6
Step 1: Understand that we have 3 different colored balls. Let's call them Ball A, Ball B, and Ball C.
Step 2: Realize that we want to find out how many different ways we can arrange these 3 balls in a line.
Step 3: Use the factorial notation to calculate the arrangements. The factorial of a number (n!) means multiplying that number by every whole number less than it down to 1.
Step 4: For 3 balls, we calculate 3! (3 factorial). This means 3 × 2 × 1.
Step 5: Calculate 3 × 2 = 6, and then multiply by 1, which is still 6.
Step 6: Conclude that there are 6 different ways to arrange the 3 different colored balls.
Permutations – The arrangement of distinct objects in a specific order, calculated using factorial notation.
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