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Question
Six P's' have to be placed in the squares of the diagram given below such that each column contains at least one P. In how many ways this can be done?
Six P's' have to be placed in the squares of the diagram given below such that each column contains at least one P. In how many ways this can be done?
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Solution
The correct option is B 26
As all X’s are identical, the question is of selection of 6 squares from 8 squares, so that no row remains empty. Here R1 has 2 squares, R2 has 4 squares and R3 has 2 squares.
The selection scheme is as follows
R1 R2 R3 1 4 1 or 1 3 2 or 2 3 1 or 2 2 2
∴ Number of selections are2 C1 x 4 C4 x 2 C1 + 2 C1 x 4 C3 x 2 C2 + 2 C2 x 4 C3 x 2 C1 + 2 C2 x 4 C2 x 2 C2=26
As all X’s are identical, the question is of selection of 6 squares from 8 squares, so that no row remains empty. Here R1 has 2 squares, R2 has 4 squares and R3 has 2 squares.
The selection scheme is as follows
R1 | R2 | R3 | |
1 | 4 | 1 | |
or | 1 | 3 | 2 |
or | 2 | 3 | 1 |
or | 2 | 2 | 2 |
∴ Number of selections are
2 C1 x 4 C4 x 2 C1 + 2 C1 x 4 C3 x 2 C2 + 2 C2 x 4 C3 x 2 C1 + 2 C2 x 4 C2 x 2 C2
=26
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