Question

In how many ways can 15 different things be divided into three groups containing 7,5 and 3 things?
​

Answer 1

Answer:

There’s a formula for division of things which you can make use of. The number of ways of dividing  m  different things into groups of sizes  a1,a2…an,  where  m=  a1+a2+….+an  is

m!a1!∗a2!∗….∗an!  

But this is only applicable when  a1≠a2≠…≠an . If  k  is the number of groups with same size then the formula is

m!(a1!∗a2!∗….∗an!)∗k!  

So in our case  m=15  and the groups are of size  5  and all  3  have the same size meaning  k=3 . So the answer is:

15!(5!∗5!∗5!)∗3!  

=1,26,126