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Q.
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
Permutations and Combinations
Solution:
Number of ways of choosing 2 parallel lines
from a set of four parallel lines $={ }^4 C_2$
Number of ways of choosing 2 parallel lines from a set of 3 parallel lines $={ }^3 C_2$
$\therefore$ Required number of ways $={ }^4 C_2 \times{ }^3 C_2$
$=\frac{4 \times 3}{2 \times 1} \times 3$
$ =6 \times 3=18$