# computation

• Apr 7th 2009, 05:02 PM
brainbaby
computation
Chinese Astrology – total combinations

12 male animals and 12 female animals = 144 combinations ???
but I need to factor in:
each could be born in one of 12 months
each could be born in one of 12 hours (yes, 12)
each could be one of five elements (earth, water, wood, metal, fire)

Is the answer – 12 x12 x 12 x 12 x 5 = 103,680
?????? I need help please :o(
Susan
• Apr 8th 2009, 12:38 AM
Combinatorics
Hello Susan
Quote:

Originally Posted by brainbaby
Chinese Astrology – total combinations

12 male animals and 12 female animals = 144 combinations ???
but I need to factor in:
each could be born in one of 12 months
each could be born in one of 12 hours (yes, 12)
each could be one of five elements (earth, water, wood, metal, fire)

Is the answer – 12 x12 x 12 x 12 x 5 = 103,680
?????? I need help please :o(
Susan

Welcome to Math Help Forum!

What you've done here is to choose a pair of animals first (and you're right there are 144 ways of doing this), and then to allocate for them a month, a time and an element.

The problem with this is that it assumes that each animal in the pair that has been chosen, has the same month, time and element. I presume that you didn't intend this (although you haven't said so), in which case you need to say:

• The male animal can be allocated a month, time and element in 12 x12 x 5 ways.
• The female animal can be allocated a month, time and element in 12 x 12 x 5 ways.

So once the pair has been chosen (in 12 x 12 ways) we allocate each member of the pair its month, time and element in (12 x 12 x 5) x (12 x 12 x 5) ways.

So the total number of choices altogether is (12 x 12) x (12 x 12 x 5) x (12 x 12 x 5) = 74 649 600