5 employees how many possible groups of 3?
From a group of 5 employees at a company, we need to select a team of 3 employees to work on a project. How many different combinations of 3 employees can be formed? The correct answer is 10, but could you please explain how this is calculated?
2 Answers
C(5, 3) = 5 4 3 / (3 2 1) = 10
there are 5 ways to select the first person for the group
there are 5 - 1 ways to select the second person for the group
there are 5 - 2 ways to select the third person for the group
we divide by 3 2 1 since we ignore any inner rearrangements within the group
Nov 24, 2024
There are 2 possibility if u didn't know about sets then,
let the 5 employees be a,b,c,d,e,
then the possible groups of 3 are
1) a,b,c
2)a,b,d
3)a,b,e
4)a,c,d
5)a,c,e
6)a,d,e
7)b,c,d
8)b,c,e
9)b,d,e
10)c,d,e
If u know sets(Class XI) then,
let A={a,b,c,d,e}
n(A)=2^5=32
in this 32,
5 are single element,
5*2=10 are double elements
5- 4 element sets (logical thinking)
1- 5 element sets
and 1 null set set
therefore groups of three are 32-5-10-5-1-1=10
therefore answer is 10
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