Microsoft Office Tutorials and References

In Depth Information

**Using MULTINOMIAL to Solve a Coin Problem**

Using

Using
MULTINOMIAL

MULTINOMIAL
to Solve a Coin Problem

to Solve a Coin Problem

Although the multinomial distribution is a fairly complex mathematical

concept, the following example illustrates a fun puzzle that can be solved

with the function.

Syntax

=MULTINOMIAL(number1,number2,...)

The MULTINOMIAL function returns the ratio of the factorial of a sum

of values to the product of factorials. The arguments number1,number2,...

are one to 255 values for which you want the multinomial. For example,

MULTINOMIAL(a,b,c,d) is (a+b+c+d)! / a!×b!×c!×d!.

Suppose that you have a huge jar that contains hundreds of pennies, nickels,

dimes, and quarters. You reach into the jar and pull out six coins. How many

possible arrangements of the coins can there be? To picture this problem, you

should sort the six types of coins from low to high. You can use three mov-

able dividers to group the coins into denominations. In the left side of
Figure

nickel, three dimes, and one quarter. It is possible to pull out none of a par-

pennies and one dime. In this case, the dividers are adjacent for nickels and

pennies. In every case, the quarter divider must always be at the bottom, so

how many ways are there to arrange the other three dividers among six coins?