A rectangle with sides of lengths (...

A rectangle with sides of lengths (2n - 1) and (2m- 1) units is divided into squares of unit length. The number of rectangles which can be formed with sides of odd length, is (a) m n (b) mn (m + 1)(n+1) (d) None of these (c) -n-1

JEE/Engineering Exams
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Total no. of vertical lines ( =2 mathrm{m} ) Total no. Of horizontal lines ( =2 n ) Now we have to find the no. of rectangles with odd sides. Let's select 1 vertical side out of ( 2 mathrm{m}: 2 mathrm{m} ) C ( 1 . ) Now another vertical side can be out of m sides only coz length of rectangle should be odd..Same goes with horizontal sides. So the answer would be ( left(2 m C 1^{*} m C 1 / 2right)^{*} ) ( left(2 n C 1^{*} n C 1 / 2right) )
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