"Day 52 of My Learning Journey: Setting Sail into Data Excellence! ⛵️ Today's Focus: Maths for Data Analysis ( Per & Comb - 7)

PERMUTATION AND COMBINATION - 7

Combination ( Or Selection )

It has two concept

Selection of different objects
Selection of alike objects.

Combination ( or selection of different objects )
Q1. Consider 4 different balls
A,B,C,D
In how many ways can we select a ZERO ball ?

Sol. There are 1 way.

Q2. Consider 4 different balls
A,B,C,D
In how many ways can we select ONE ball ?

Sol. There are 4 ways.

Q3. Consider 4 different balls
A,B,C,D
In how many ways can we select TWO balls ?

Sol. There are 6 ways.
AB , BC, AC, AD, BD, CD

Q4. Consider 4 different balls
A,B,C,D
In how many ways can we select THREE balls ?

Sol. There are 4 ways.
ABC, BCD, ABD, ACD

Q5. Consider 4 different balls
A,B,C,D
In how many ways can we select FOUR balls ?

Sol. There are 1 way.
ABCD

SELECTION
HERE EQUATING (=) HELP US TO KNOW THE NO. OF WAYS.
0 = ALL ( 1 WAY )
1 = N-1
2 = N-2
3 = N-3

100 BALLS
IN HOW MANY WAYS WE CAN SELECT ZERO BALLS = 1 WAYS
IN HOW MANY WAYS WE CAN SELECT ONE ABLLS = 100 WAYS
IN HOW MANY WAYS WE CAN SELECT TWO BaLLS =

Now it is interesting

100 * 99 / 2! * 98!

While selection arrangement does not count.

In how many ways we can select ‘r’ balls = 100! / r! * ( 100-r )!

In general = n! / r! * ( n-r)! = nCr

Total number of ways of selection of ‘r’ different objects out of n- different objects.

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