To find out how many ways 8 people can be paired up, we first need to understand the pairing process. If we have 8 people, we can think of the pairing as grouping them into 4 pairs.
One way to approach this is to use the formula for pairing n people:
Number of ways to pair = (n!)/(2^(n/2) * (n/2)!)
In our case, n = 8. Plugging in the values:
Number of pairs = (8!)/(2^(8/2) * (8/2)!) = (8!)/(2^4 * 4!)
Calculating this step-by-step:
1. Calculate 8! = 40320
2. Calculate 4! = 24
3. Calculate 2^4 = 16
Now substitute these values back into the formula:
Number of pairs = 40320 / (16 * 24)
4. Multiplying 16 and 24 gives us 384:
Number of pairs = 40320 / 384 = 105
Thus, there are 105 ways to pair up 8 people.