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Number of arrangements of 10 different things Taken 4 at a time in which one particular thing only occurs always occurs?
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Number of arrangements of 10 different things Taken 4 at a time in whi...
Introduction
To find the number of arrangements of 10 different things taken 4 at a time in which one particular thing only occurs always occurs, we need to use the concept of permutations.
Solution
We can break down the solution into the following steps:
- Select the particular thing that always occurs. There are 10 choices for this.
- Select 3 other things from the remaining 9 things. This can be done in 9C3 ways.
- Arrange the 4 things (including the particular thing) in 4! ways.
Therefore, the total number of arrangements is:
10 * 9C3 * 4!
Simplifying this expression, we get:
10 * (9*8*7)/(3*2*1) * 4*3*2*1
= 10 * 84 * 24
= 20,160
Therefore, there are 20,160 arrangements of 10 different things taken 4 at a time in which one particular thing always occurs.
Explanation
We first select the particular thing that always occurs because this limits the number of choices for the remaining 3 things. We then select the 3 other things from the remaining 9 things using the combination formula (9C3) because order does not matter at this point. Finally, we arrange the 4 things (including the particular thing) in 4! ways because order matters at this point. By multiplying these three quantities, we get the total number of arrangements.
Community Answer
Number of arrangements of 10 different things Taken 4 at a time in whi...
Answer is 2016
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Number of arrangements of 10 different things Taken 4 at a time in which one particular thing only occurs always occurs?
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Number of arrangements of 10 different things Taken 4 at a time in which one particular thing only occurs always 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 Number of arrangements of 10 different things Taken 4 at a time in which one particular thing only occurs always occurs? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Number of arrangements of 10 different things Taken 4 at a time in which one particular thing only occurs always occurs?.
Number of arrangements of 10 different things Taken 4 at a time in which one particular thing only occurs always 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 Number of arrangements of 10 different things Taken 4 at a time in which one particular thing only occurs always occurs? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Number of arrangements of 10 different things Taken 4 at a time in which one particular thing only occurs always occurs?.
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