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