In how many ways can 12 prizes be divided between 2 people? (combination question)
To find the number of ways to divide 12 prizes between 2 people, we can use the concept of combinations. In this case, we want to know the number of combinations of 12 prizes taken 2 at a time (or, in other words, how many ways can we choose 2 prizes out of 12).
To calculate combinations, we can use the formula:
C(n, r) = n! / (r!(n-r)!)
Where:
C(n, r) represents the number of combinations of n items taken r at a time,
n! represents the factorial of n (the product of all positive integers from 1 to n),
r! represents the factorial of r, and
(n-r)! represents the factorial of (n-r).
In this case, we want to find C(12, 2), which can be calculated as follows:
C(12, 2) = 12! / (2!(12-2)!)
= 12! / (2! * 10!)
= (12 * 11 * 10!) / (2! * 10!)
= (12 * 11) / 2
= 6 * 11
= 66
Therefore, there are 66 ways to divide 12 prizes between 2 people.