5C5 is equivalent to ________________?
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Answer: C. 1
Explanation
The combination formula nCr evaluates to 1 when n equals r. Choosing all five items out of five available items can be done in exactly one way. Mathematical evaluation of 5C5 yields a numerator and denominator of 120. Combinations calculate the number of ways to select items where order does not matter. The formula for combinations is n factorial divided by r factorial times n minus r factorial. Any set has exactly one subset containing all of its elements.
Probability calculations frequently encounter boundary conditions where choosing all elements equals one. Combinatorial mathematics uses binomial coefficients for counting sample space outcomes. Understanding combinations prevents common arithmetic errors in discrete probability problems. 5 represents the result of calculating 5C1 rather than 5C5 combinations. 5x5 represents multiplication of independent choices rather than a combinatorial selection. None of these is incorrect because option C provides the exact correct value.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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