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Six X ' s have to be placed in thesquare...

Six X ' s have to be placed in thesquares of the figure below, such that each rowcontains atleast one X. In how many different wayscan this be done?

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The correct Answer is:
26
As all the X's are identical, the question is of selection of 6 squares from 8 squares, so that no row remains empty. Here `R_(1)` has 2 squares, `R_(2)` has 4 squares and `R_(3)` 2 squares. The selection scheme is as follows :

`therefore` Number of selections are `= . ^(2)C_(1)xx .^(4)C_(4)xx .^(2)C_(1)+ .^(2)C_(1)xx .^(4)C_(3)xx .^(2)C_(2)+ .^(2)C_(2)xx .^(4)C_(3)xx .^(2)C_(1)+ .^(2)C_(2)xx .^(4)C_(2)xx .^(2)C_(2)`
=4+8+8+6=26
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