Question

# The number of the rectangles excluding squares that can be formed from a rectangle of size 9×6 if it is divided by set of parallel lines of unit length as shown in the diagram is

A
391
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B
791
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C
842
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D
None of these
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Solution

## The correct option is D 791Here, l=9 and b=6 Number of rectangles that can be selected without any restrictions is =7C2×10C2 Now the squares can be selected of dimensions r×r (where r∈{1,2,...,6}) Now square of dimension 1×1 can be selected in 9×6 ways. Similarly, square of dimension 2×2 can be selected in 8×5 ways. Similarly, square of dimension 6×6 can be selected in 4×1 ways. So the number of squares will be 6∑r=1(10−r)(7−r) ∴ Number of required ways =7C2×10C2−6∑r=1(10−r)(7−r) =945−6∑r=1(70−17r+r2) =945−(70×6−17×21+91)=791

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