First slide

Combinations

Question

A rectangle with sides 2m - 1 and 2n - 1 divided into squares of unit length. The number of rectangle which can be formed with sides of odd
length is

Moderate

A

m²n²
B

mn (m+1)(n+1)
C

4^m+n-1
D

None of the above

Solution

For length. number of choices is $(2 m - 1) + (2 m - 3) + \dots + 3 + 1 = m^{2}$
Similarly. for breadth number of choices is $(2 n - 1) + (2 n - 3) + \dots + 3 + 1 = n^{2}$
Hence, required number of choices is m²n²,

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