Combination Formulas

Factorial of n,n! :

The Combinations formula:

factorial formula

 

Important formulas on Combinations:

nc0 = 1

ncn = 1

ncr = ncn-r

The number of groups (combinations) of n different things taking any number at a time is:

nc0 + nc1 + nc2 +….. ncn = 2n – 1

 

  • The number of ways (alternatively groups or combinations) in which n things can be divided into p things and q things is

combinations formula

 

  • The number of ways (alternatively groups or combinations) in which 3n can be divided equally into three distinct groups each having n things is

3n is divided equally into 3 distinct groups

 

  • The number of ways (alternatively groups or combinations) in which 3n can be divided equally into three identical groups each having n things is

3n is divided equally into 3 identical groups

 

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