how many ways can 5 people be selected in an organization
Your School SUBJECT is MATH.
If there are n to choose from, then that is
P(n,5) or C(n,5)
To calculate the number of ways to select 5 people in an organization, you need to consider if the order matters (permutations) or if it does not matter (combinations).
If the order matters (permutations):
In this case, you are selecting 5 people from a group. The number of ways to select k items from a group of n items, where the order matters, is given by the formula:
nPk = n! / (n-k)!
In this case, n is the total number of people in the organization (assuming it is larger than or equal to 5) and k is the number of people you want to select (in this case, 5).
Therefore, plugging in the values, the calculation would be:
nPk = n! / (n-k)!
= 5! / (5-5)!
= 5! / 0!
The value of 0! (zero factorial) is defined as 1, so the equation becomes:
nPk = 5! / 1
= 5!
Therefore, there are 5! (5 factorial) ways to select 5 people in an organization, where the order matters.
If the order does not matter (combinations):
In this case, you are selecting 5 people from a group, but the order in which they are selected does not matter.
The number of ways to select k items from a group of n items, where the order does not matter, is given by the formula:
nCk = n! / (k! * (n-k)!)
In this case, n is the total number of people in the organization (assuming it is larger than or equal to 5), and k is the number of people you want to select (in this case, 5).
Therefore, plugging in the values, the calculation would be:
nCk = n! / (k! * (n-k)!)
= 5! / (5! * (5-5)!)
= 5! / (5! * 0!)
The value of 0! (zero factorial) is defined as 1, so the equation becomes:
nCk = 5! / (5! * 1)
= 5! / 5!
= 1
Therefore, there is only 1 way to select 5 people in an organization, where the order does not matter.