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Using MULTINOMIAL to Solve a Coin Problem
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.
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
11.28 , for example, you ve arranged the dividers to indicate one penny, one
nickel, three dimes, and one quarter. It is possible to pull out none of a par-
ticular coin. In the image on the right in Figure 11.28 , you ve pulled out five
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?
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