PERMUTATION AND COMBINATION - 9
Alike Objects
Permutation of Alike Objects :-
Arrangement :-
Q1. 4 objects ( alike ) in how many ways can you arrange them ?
AAAA only in 1 way.
Explanation :-
No. of arrangements if they are different = 4!
But in this case all are alike so, = 4! / 4! = 1
Q2. 3 objects and other 2 objects( alike ) in how many ways can you arrange them ?
AAABB
Explanation :-
No. of arrangements if they are different = 5!
But in this case all are alike so, = 5! / 3! * 2!
Q3.A,A,B,B,B,C,C,D,D,D,D
In how many ways can you arrange them ?
Explanation :-
No. of arrangements if they are different = 11!
But in this case all are alike so, = 11! / 2! * 3! * 2! * 4!
WHY WE DIVIDE to get the correct answer because they are not the same.
Combination of Alike Objects :-
Selection :-
Q1. consider some objects
A,A,B,B,B,C,C?
IN HOW MANY WAYS WE CAN SELECT ONE OBJECT ?
NO. OF UNIQUE OBJECTS
IN HOW MANY WAYS WE CAN SELECT TWO OBJECTS ?
Bucket method :-
1 bucket - AA
2 bucket - BBB
3 bucket - CC
WE HAVE TO USE A BUCKET METHOD.
BOTH DIFFERENT - 3c2
BOTH ALIKE - 3c1
3C2 MEANS there are 3 buckets and we need both to be different so, at least we need to select 2 buckets where we can select different objects.
IN HOW MANY WAYS WE CAN SELECT THREE OBJECTS ?
Bucket method :-
1 bucket - AA
2 bucket - BBB
3 bucket - CC
WE HAVE TO USE A BUCKET METHOD.
ALL DIFFERENT - 3c3
ONE ALIKE TWO DIFFERENT - 3c1 * 2c1
ALL SAME - 1
This is the last CLASS for Permutation and Combination.
From Today Onwards I will be Starting Probability.
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