Combinations
If C(n, 4) = C(n, 6), then n equals
Select the correct option:
Solution
10
- Property of Combinations: (rn)=(n−rn).
- Apply Property: This implies that if (rn)=(kn), then either r=k or r+k=n.
- Solve for n:
- Since 4=6, it must be that 4+6=n.
- Therefore, n=10.
- Verification: (410)=4!6!10! and (610)=6!4!10!. They are identical.
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About This Question
- Subject
- mathematics
- Chapter
- permutations and combinations
- Topic
- combinations
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
10
- Property of Combinations: (rn)=(n−rn).
- Apply Property: This implies that if (rn)=(kn), then either r=k or r+k=n.
- Solve for n:
- Since 4=6, it must be that 4+6=n.
- Therefore, n=10.
- Verification: (410)=4!6!10! and (610)=6!4!10!. They are identical.
This easy difficulty mathematics question is from the chapter permutations and combinations, covering the topic of combinations. It appeared in the 2025 exam.
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