In how many ways can 3 red balls and 2 blue balls be arranged in a row?
Practice Questions
1 question
Q1
In how many ways can 3 red balls and 2 blue balls be arranged in a row?
10
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25
The total arrangements = 5! / (3! * 2!) = 10.
Questions & Step-by-step Solutions
1 item
Q
Q: In how many ways can 3 red balls and 2 blue balls be arranged in a row?
Solution: The total arrangements = 5! / (3! * 2!) = 10.
Steps: 9
Step 1: Count the total number of balls. We have 3 red balls and 2 blue balls, which gives us a total of 5 balls.
Step 2: Understand that we need to arrange these 5 balls in a row.
Step 3: If all the balls were different, we could arrange them in 5! (5 factorial) ways. 5! means 5 x 4 x 3 x 2 x 1 = 120.
Step 4: However, we have identical balls. We have 3 red balls that are the same and 2 blue balls that are the same.
Step 5: To account for the identical balls, we divide by the number of arrangements of the identical balls. For the 3 red balls, we divide by 3! (3 factorial), which is 3 x 2 x 1 = 6.
Step 6: For the 2 blue balls, we divide by 2! (2 factorial), which is 2 x 1 = 2.
Step 7: Now, we calculate the total arrangements using the formula: Total arrangements = 5! / (3! * 2!).
Step 8: Plug in the values: Total arrangements = 120 / (6 * 2) = 120 / 12 = 10.
Step 9: Therefore, the total number of ways to arrange 3 red balls and 2 blue balls in a row is 10.
