The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of four parallel lines, is

(a) 18
(b) 24
(c) 32
(d) 36 ✓ UPSC's answer

Why the answer is (d)

• A parallelogram is formed by selecting exactly two lines from the first set of four parallel lines and exactly two lines from the second set of four parallel lines.

• The number of ways to choose 2 lines from the first set of 4 is calculated using the combination formula C(4, 2) = 4! / (2! * 2!) = 6.

• Similarly, the number of ways to choose 2 lines from the second set of 4 is C(4, 2) = 6.

• Since the choices are independent, the total number of parallelograms is the product of the two combinations: 6 * 6 = 36.

• Therefore, the correct answer is 36, which corresponds to option (d).

Why the other options are wrong

(a) 18: 18 is incorrect because it does not equal the product of the combinations C(4,2) * C(4,2).
(b) 24: 24 is incorrect because it is not the result of multiplying the number of ways to choose two lines from each set.
(c) 32: 32 is incorrect because it is not the product of the combinations C(4,2) and C(4,2).

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.