COMBIN( ) and PERMUT( ): Figuring Combinations and Permutations

COMBIN( ) and PERMUT( ): Figuring Combinations and Permutations
People use the COMBIN( ) and PERMUT( ) functions in probability theory, to count the number of possible outcomes when randomly choosing items from a set. COMBIN( ) and PERMUT( ) are short for combinations and permutations, which are mathematical terms for the number of distinct combinations you can make from a set of items. The main difference lies in the way they consider the order of items in a set (more on that in a moment).

One reason you might use COMBIN( ) and PERMUT( ) is to assess the odds in a game of chance. You could use COMBIN( ) to help you figure out, say, the odds of being dealt an ace of spades from a deck of cards. And people often use both these functions to calculate the occurrence of other random events, like winning the lottery or being hit by a falling anvil.

Both COMBIN( ) and PERMUT( ) take two arguments. The first argument is the number of different items in your set. The second argument is the number of items you're randomly selecting each time you "draw" from the set. For example:
 COMBIN(number_in_set, number_chosen)


The key difference between COMBIN() and PERMUT( ) is that PERMUT( ) assumes order is important, while COMBIN( ) assumes it isn't. For example, say you want to count how many possible ways you can draw five cards from a 52-card deck.

You'd use the PERMUT( ) function as shown here:
 =PERMUT(52,5)


PERMUT( ) generates a whopping result of 311,875,200 because it counts every group of five cards as unique, even if the difference is only a matter of card order. Thus, the set 1, 2, 3, 4, 5 is different, for PERMUT( ), from 5, 4, 3, 2, 1.

By contrast, when COMBIN( ) evaluates those same parameters, it returns a value of 2,598,960.

As you can see, permutations are far more plentiful than combinations. In fact, you can convert the number of combinations into the number of permutations by multiplying it by 5! (5*4*3*2*1), which is a measure of how many different ways you can arrange the order of five different items.

To go much further with PERMUT( ) and COMBIN( ), you'll need a refresher course in probability theory. However, you may be interested to know that you can find the probability of an event by dividing the number of satisfactory outcomes (the number of outcomes that meet your criteria) into the number of total outcomes (the total number of possibilities). For example, the chance of your getting a specific hand of cards is expressed like so:
 =1/COMBIN(52,5)


Here, you're only interested in a single outcome (a hand that has every card you want). Thus, there's one satisfactory outcome. You can use the COMBIN( ) function to find the total number of possibilities by counting the different possible draws.

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