1 Answer | Add Yours
This problem is a common one in a probability course. We are trying to count the number of possibilities to arrange people in a certain order. They will all be jumping, so there are no tricks here!
To start, set up the number of positions that each person may take:
____ _____ _____ _____ _____
In the first position, there are 5 people that may volunteer to go first. For each possibility here, there are 4 more people that can take the second position, 3 more for the third position, and so on. This gives us the following relation, where `P` is the number of possibilities:
`P = 5*4*3*2*1 = 5!`
The `!` operator is the "factorial" operator. It simply means we multiply the number by every other number before it until we hit 1. Evaluating the factorial gives us the following result:
`P = 120`
There are many problems like this where only 3 people are jumping or 2 people or what-have-you. In this case, there is a function used in probability called "permutation." It is given by the following formula, where `n` is the number of people and `k` is the number of possible positions:
`_n P_k = (n!)/((n-k)!)`
We can use this formula, too, to calculate the number of ways for people to jump:
`P = _5 P_5 = (5!)/((5-5)!) = (5!)/(0!) = 5! = 120`
Notice that ` 0! = 1`. This relationship is critical to understand many of these sorts of formulas.
Again, our final answer is 120 possible permutations of people diving.
We’ve answered 319,852 questions. We can answer yours, too.Ask a question