Microsoft Office Tutorials and References
In Depth Information
Combining
Combining
Combinations are similar to permutations but with a distinct difference.
The order of items is intrinsic to permutations. Combinations, however, are
groupings of items when the order doesn’t matter. For example, “John Paul
George Ringo” and “Ringo George Paul John” are two distinct permutations
but identical combinations.
Combinations are grouping of items, regardless of the order of the items.
The syntax for the function follows:
=COMBIN(total number of items, number of items to use)
The first argument is the total number of items to choose from, and the
second argument is the number of items to be used in determining the
combinations. The function returns a single whole number. The arguments for
the COMBIN function are the same as those for the PERMUT function. The
first argument must be equal to or greater than the second argument.
Plugging in the number 4 for both arguments — COMBIN(4,4) — returns 1.
Yes, there is just one combination of four items selected from a total of four
items! Using the Beatles once again, just one combination of the four
musicians exists, because the order of names doesn’t matter.
Selecting to use two items from a total of four — COMBIN(4,2) — returns 6.
Selecting two items out of two — COMBIN(2,2) — returns 1. In fact,
whenever the two arguments to the COMBIN function are the same, the result is
always 1.
Raising Numbers to New Heights
There is an old tale about a king who loved chess so much he decided to
reward the inventor of chess with any request he had. The inventor asked for
a grain of wheat for the first square of the chessboard on Monday, two grains
for the second square on Tuesday, four for the third square on Wednesday,
eight for the fourth square on Thursday, and so on, each day doubling the
amount until the 64th square was filled with wheat. The king thought this was
a silly request. The inventor could have asked for riches!
What happened is that the kingdom quickly ran out of wheat. By the
15th day, the number equaled 16,384. By the 20th day, the number was
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