number of groups taking 13 cards out of 52 cards (order of groups is important) =52!divided by (13!)^4

but number of groups taking 13 cards out of 52 cards (order of groups is not important) = 52!divided by{ 4!(13!)^4 }

how?

see one more example

number of groups taking 11,12,13,16 cards out of 52 cards (order of groups is important) =52!divided by (11!*12!*13!*16!*)

but number of groups taking 11,12,13,16 cards out of 52 cards (order of groups is not important) = ??????

please explain answer with reasons.

well its quite simple

1) Case

52 cards equally divided among 4 groups (order is important) ( it should be players instead of groups)

and it goes like this

⁵²C₁₃ x ³⁹C₁₃ x ²⁶C₁₃ x ¹³C₁₃ x 4!/4!

solving it we get

52!/13!⁴

now multiplication by 4! because order is important

division by 4! because as the players have equal no of cards

2) Case

52 cards equally divided among 4 groups (order is important)

⁵²C₁₃ x ³⁹C₁₃ x ²⁶C₁₃ x ¹³C₁₃ /4!

52!/13!⁴ x 1/4!

Divide by 4! as the groups have equal no of cards

Note - ORDER IS NOT RELEVANT FOR GROUPS SO WE DIDNT MULTIPLY BY 4!

Hope i helped

any queries message me..!