Simple Probability Question

[jack]

Amongst 5 home owners, a committee of 2 has to be formed. How many such different committees can be formed?
a) 20
b) 5
c)10
d)25

[Arushi :))]

Its 5C2= 5*4/2= 10

[jack]

Why did't you do like that?
1st person can occupy any one of the 5 positions and 2nd person can occupy any one of the remaining 4 positions
so 5*4=20

[The Villain]

ans is c

[Arushi :))]

@ jack,
You are using permutation here, which is wrong.
Remember, we are forming a committee here and order of persons doesn't matter.
If you are doing it this way, then don't forget to divide it by 2.
Because,
Consider the case where first position is occupied by A and second by B, and another case where first position is occupied by B and second by A.
So these two are equivalent.
Here, order doesn't matter.
So divide your answer by 2.