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The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is?
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The number of arrangements of 10 different things taken 4 at a time in...
Understanding the Problem
To find the number of arrangements of 10 different things taken 4 at a time, where one specific item must always be included, we can break down the problem as follows:
Step 1: Fix the Particular Item
- Since one particular item must always be included, we can consider that item as a constant.
- This leaves us needing to choose 3 more items from the remaining 9 items.
Step 2: Choose Additional Items
- From the remaining 9 items, we need to select 3 items.
- The number of ways to choose 3 items from 9 is given by the combination formula "9 choose 3".
Step 3: Calculate Arrangements
- After selecting the 3 items, we now have 4 distinct items (including the fixed one).
- The number of arrangements of 4 distinct items is given by 4! (4 factorial).
Calculating the Result
- Calculate the number of combinations:
- 9 choose 3 = 9! / (3!(9-3)!) = 84
- Calculate the arrangements of the chosen items:
- 4! = 24
- Now, multiply the two results:
- Total arrangements = 84 * 24 = 2016
Final Result
- Therefore, the total number of arrangements of 10 different things taken 4 at a time, where one specific item always occurs, is 2016.
To find the number of arrangements of 10 different things taken 4 at a time, where one specific item must always be included, we can break down the problem as follows:
Step 1: Fix the Particular Item
- Since one particular item must always be included, we can consider that item as a constant.
- This leaves us needing to choose 3 more items from the remaining 9 items.
Step 2: Choose Additional Items
- From the remaining 9 items, we need to select 3 items.
- The number of ways to choose 3 items from 9 is given by the combination formula "9 choose 3".
Step 3: Calculate Arrangements
- After selecting the 3 items, we now have 4 distinct items (including the fixed one).
- The number of arrangements of 4 distinct items is given by 4! (4 factorial).
Calculating the Result
- Calculate the number of combinations:
- 9 choose 3 = 9! / (3!(9-3)!) = 84
- Calculate the arrangements of the chosen items:
- 4! = 24
- Now, multiply the two results:
- Total arrangements = 84 * 24 = 2016
Final Result
- Therefore, the total number of arrangements of 10 different things taken 4 at a time, where one specific item always occurs, is 2016.
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The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is?
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The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is? 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 arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is?.
The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is? 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 arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is?.
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