There are 12 signs of the Zodiac. How many unique pairs are possible? I know this is a simple statistical problem that most high school seniors could do in their sleep but it has been 35 years since I took a math class and I just can't remember.
2007-02-24 01:53:27 · 3 answers · asked by pyro_alchemist 2 in Science & Mathematics ➔ Mathematics
Do you mean a pair with or without replacement?
If it is without replacement, the answer is 66, or C(12,2), the number of combinations of 12 things taken 2 at a time
However, perhaps you mean to include pairs such as:
Scorpio - Scorpio, which would allow replacement.
In that case there are 66 + 12 = 78
You can also think about this answer another way:
12 signs numbered 1 - 12.
#1 can be paired with each of 1 - 12, so 12 pairs.
#2 has already been paired with #1, so #2 can be paired with 2 - 12 or 11 pairs.
#3 can be paired with 3 - 12 or 10 pairs,
#4 can be paired with 4 - 12 or 9 pairs.
etc.
So the answer is 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 78
2007-02-24 02:04:50 · answer #1 · answered by Scott R 6 · 2⤊ 0⤋
There are 66 possible combinations.
The formula to be used is
nCr = n!/ [r!(n-r)! ] where n is the number of objects and r is the number of permutations of each set taken so n becomes 12 in this case and r is 2.
The link below gives a refresher course in permutations and combinations. :) Hope this helps!
2007-02-24 02:08:05 · answer #2 · answered by apspublic 2 · 0⤊ 1⤋
There are 78 possible pairs
2007-02-24 02:08:19 · answer #3 · answered by Anonymous · 0⤊ 0⤋