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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.


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.


Grade:12

1 Answers

Aditya Verma
33 Points
8 years ago

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 26C13 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..!

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