Mathematics

Question

How many ways you select 20 people from 30 people and divide them into 2 group of 10 each?

Create team A & B which is selected from 20 people thpse selected from 30 cricketers?

 

is there any differnce between  them?

please help in this

Answer 1

Yes the first problem is on division (order of groups does not matter) and the second one is distribution(order of groups matters)..

Solution to 1st problem :

So first we select 20 persons from 30 persons which can be done in ³⁰C₂₀ ways..Having done that now for division of 20 persons into 2 equal teams with no team names means no distinction which is done in : (20!) / [(10!)² .2!] ways..

So total no of required ways  =  ³⁰C₂₀  *  (20!) / [(10!)² . 2!]

Solution to 2nd problem :

Here the only difference w.r.t previous one is we have team names ..So order of teams matter here..Hence the result in previous one will be multiplied by 2! to get the no of ways of distribution :

Hence no of required ways  =  ³⁰C₂₀  *  (20!) / [(10!)² . 2!] * 2!

                                        =  ³⁰C₂₀  *  (20!) / (10!)² 

Comments

thanks @Habib

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Fortunately I did the same thing..but one doubt I have that is in second ques nothing is mentioned about number of players in each team .cricket team has 11 players though at Least. Generally should be equally divided.But what if nothing is mentioned about team division.