permutation and combination

Question

How many to divide 2t objects?

A. 2 groups of t each

B. t groups of 2 each

Comments

@sonam , for 2^nd  part  , I got [C(2t,2)*C( 2t-2 , 2)* C(2t-4 , 2)*.....C(2,2) ] / (t!) .. I think, it is correct and ur answer is also correct...Then how to prove that [C(2t,2)*C( 2t-2 , 2)* C(2t-4 , 2)*.....C(2,2) ] = (2t)!/(2)^t...Could u please help..

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by putting some values :P

i am also finding ..wait :)

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Assuming the objects are labeled :

If the group's are not labeled :

1. C(2t, t)*C(t, t) = C(2t, t)

2. C(2t, 2)*C(2t-2, 2)*...C(2, 2) = ((2t)!)/(2^t)

If the groups are labeled :

1. C(2t, t)*(2!)

2. ((2t)!*(t!))/(2^t)

Pls Correct me if I'm wrong