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"Day 54 of My Learning Journey: Setting Sail into Data Excellence! Today's Focus: Maths for Data Analysis ( Perm & Comb - 9)

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
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IN HOW MANY WAYS WE CAN SELECT TWO OBJECTS ?

Bucket method :- 
 1 bucket - AA 
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2 bucket - BBB
3 bucket - CC

WE HAVE TO USE A BUCKET METHOD. 
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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. 
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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.

Feel free to share this post to enhance awareness and understanding of these fundamental concepts in statistical analysis!

🙏 Thank you all for your time and support! 🙏

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