What is the output of MS-Excel function = COMBIN (4, 2) ?

Question

Accepted Answer

The correct option is (2):
The MS-Excel function =COMBIN(n, k) is explicitly designed to calculate the number of combinations, which represents the number of ways to choose *k* items from a total set of *n* items where the order of selection does not matter. In this case, the function is =COMBIN(4, 2), where $n=4$ (the total number of items) and $k=2$ (the number of items to choose). The mathematical formula for combinations is $C(n, k) = \frac{n\!}{k\!(n-k)\!}$. Substituting the values gives $C(4, 2) = \frac{4\!}{2\!(4-2)\!} = \frac{4 \times 3 \times 2 \times 1}{(2 \times 1)(2 \times 1)} = \frac{24}{4}$, which results in 6. Therefore, the function correctly outputs 6, as it is the exact number of unique ways two items can be selected from a group of four without concern for the arrangement.

The incorrect option is (1):
Option 8 is an incorrect answer because it does not correspond to the result of the combination formula. A value of 8 might arise from a simple arithmetic mistake or an arbitrary multiplication like $4 \times 2$. The nearest similar calculation, Permutation $P(4, 2)$, which is $4 \times 3$, yields 12. Since the combination formula is a specific calculation method rooted in probability and counting theory, 8 is simply not the correct mathematical outcome for choosing 2 items from 4.

The incorrect option is (3):
The value 16 is mathematically equivalent to $4^2$. This calculation represents the number of possible outcomes if two items were chosen from four *with replacement* and *with order mattering*. Since the COMBIN function specifically calculates combinations *without replacement* and *without regard to order*, 16 is based on a fundamentally different counting principle (selections with repetition) and is, therefore, an incorrect output for the given function.

The incorrect option is (4):
The output value 2 is merely the parameter *k* (the number of items being chosen from the set of *n* items) passed into the function, but it is not the actual result of the combinatorial calculation. The function's purpose is to determine the *total number of distinct sets* of 2 items that can be selected from the total group of 4, not just to return the count of items being selected. Thus, 2 represents an input argument, not the final combinatorial output.