QuestionHow many ways can 35 new employees be grouped into sets of 5 without repetition? Use the formula for combinations: .
Studdy Solution
STEP 1
Assumptions1. The total number of new employees is35.
. We want to form groups of5 employees.
3. Each employee can be in exactly one group.
4. The order of employees within a group does not matter (i.e., group ABCDE is the same as groupDCBA).
STEP 2
This is a combination problem, as we are selecting groups where order does not matter. The formula for combinations is given bywhere- is the total number of items, - is the number of items to choose, - is the factorial of (the product of all positive integers up to ), - is the factorial of , and- is the factorial of .
STEP 3
Now, plug in the given values for and into the combination formula.
STEP 4
implify the expression in the denominator.
STEP 5
Calculate the factorials in the denominator.
STEP 6
Calculate the factorial in the numerator.
STEP 7
Perform the division to find the number of ways to form groups of5 employees.
So, there are324,632 different groups of5 new employees that can be made without repetition.
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