First slide

Permutations

Question

Six X's have to be placed in the square of the figure such that each row contains atleast one 'X'. In how many different ways can this be done?

Moderate

A

28
B

27
C

26
D

None of these

Solution

In all, we have 8 squares in which 6 'X .have to be placed and it can be done in $^{8} C_{6} = 28$
But this includes the possibility that either the top or horizontal row does not have any X.
Since, we want each row must have atleast one .x, these two possibilities are to be excluded.
Hence, required number of ways = 28 - 2 = 26

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