Question

Please answer this.......

Answer 1

Hmm...this one is really an interesting question.

First of all forget about the remaining 76 horizontal dominoes. Because as the vertical 2 dominoes are fixed on their places , the horizontal one will be automatically arranged.

Now we just have to find out number of ways to arrange two vertical dominoes in the grid.

We can find number of ways of the arrangement by using Permutation & Combination

First let's consider the case when the two dominoes are placed suct that they occupying 1st and 2nd row.

Here we have 52 places where we can place thsese 2 dominoes.

No. of ways in which we can select 2 places out of 52 is given by
= 52C2
= [52!]/[(52-2)!(2!)]
=(52x51)/2
=1326

Now we have to remove the cases where the spaces between the two dominoes are in odd number.
=1326/2
=663

Now we have to consider the cases in which the dominoes are placed in 2nd and 3rd row.
= 663x2
=1326

So the total number of ways are = 1326