#DS Inserting elements into Min Heap?

Question

The number of distinct min heap are possible with keys 1, 2, 3, 4, 5 are ________.

I know, there are variance of this question for Max heap and even for Min heap, the answer won't change, but I just wanna know if my technique is right or not. 

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Since it's a Min heap, the minimum value will be at root. 

This will be the min heap as  

                                 o   -------> root will be chosen in 1 way
                                / \
                               o   o 
                              / \ 
                             o  o

-> Left sub tree will be **4C3*1*2** way as again root will get min value and left and right child can get any value. 

-> Lastly the right sub tree => 1C1 = 1 

Totally - 1*4C3*1*2*1 = 8. Is this approach correct?

Comments

shouldn't be left sub tree 4C3*1*2?

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Yes, indeed, wrongly typed. It's 4C3*1*2. Then is it correct?

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yes then correct.

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Thanks Gupta Ji! :)

Answer 1

4c2*1*1

Comments

I think wrong answer

 Answer is 8