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The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs?
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The number of permutations of 10 different things taken 4 at a time in...
Understanding the Problem
To find the number of permutations of 10 different things taken 4 at a time, where one specific item is excluded, we can approach the problem systematically.
Step 1: Determine the Remaining Items
- From the original 10 items, we exclude the specific item.
- This leaves us with 9 items to choose from.
Step 2: Calculate the Permutations
- We are now looking for the number of ways to arrange 4 items from these 9 remaining items.
- The formula for permutations of n items taken r at a time is given by n! / (n - r)!.
Step 3: Apply the Formula
- Here, n = 9 (remaining items) and r = 4 (items to arrange).
- Thus, we calculate:
- Permutations = 9! / (9 - 4)!
- This simplifies to 9! / 5!.
Step 4: Perform the Calculation
- Expanding the factorials, we get:
- 9! = 9 × 8 × 7 × 6 × 5!
- The 5! cancels out, leading to:
- Permutations = 9 × 8 × 7 × 6.
Final Calculation
- Now we multiply:
- 9 × 8 = 72
- 72 × 7 = 504
- 504 × 6 = 3024.
Conclusion
- Therefore, the total number of permutations of 10 different items taken 4 at a time, with one specific item excluded, is 3024.
To find the number of permutations of 10 different things taken 4 at a time, where one specific item is excluded, we can approach the problem systematically.
Step 1: Determine the Remaining Items
- From the original 10 items, we exclude the specific item.
- This leaves us with 9 items to choose from.
Step 2: Calculate the Permutations
- We are now looking for the number of ways to arrange 4 items from these 9 remaining items.
- The formula for permutations of n items taken r at a time is given by n! / (n - r)!.
Step 3: Apply the Formula
- Here, n = 9 (remaining items) and r = 4 (items to arrange).
- Thus, we calculate:
- Permutations = 9! / (9 - 4)!
- This simplifies to 9! / 5!.
Step 4: Perform the Calculation
- Expanding the factorials, we get:
- 9! = 9 × 8 × 7 × 6 × 5!
- The 5! cancels out, leading to:
- Permutations = 9 × 8 × 7 × 6.
Final Calculation
- Now we multiply:
- 9 × 8 = 72
- 72 × 7 = 504
- 504 × 6 = 3024.
Conclusion
- Therefore, the total number of permutations of 10 different items taken 4 at a time, with one specific item excluded, is 3024.
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The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs?
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The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs?.
The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs?.
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