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The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines, is
  • a)
    6
  • b)
    18
  • c)
    12
  • d)
    9
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The number of parallelograms that can be formed from a set of four par...
This is nothing but 4C2 x 3C2.
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The number of parallelograms that can be formed from a set of four par...
Solution:

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is equal to the number of ways in which we can choose any two lines from each set of parallel lines.

Thus, the number of parallelograms = Number of ways of choosing 2 lines from 4 parallel lines × Number of ways of choosing 2 lines from 3 parallel lines

= (4C2) × (3C2)

= 6 × 3

= 18

Hence, the correct answer is option B, i.e., 18.
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Solution:Given, a cube coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size.Number of smaller cubes in a row = 5Total number of smaller cubes = 125Let's consider the cube orientation as shown below:``` ________ | | | U1 | |_______ | / /| / F1 / | /________/ | | | R1 | | L1 |___| |________|/ D1```U1, F1, R1, L1, D1 are the faces of the cube and they are coloured as follows:- U1 : Uncoloured- F1 : Pink- R1 : Silver- L1 : Uncoloured- D1 : OrangeNow, let's count the number of cubes that are coloured silver on one face, orange or pink on another face, and have four uncoloured faces.- We can select the face opposite to the silver face in 2 ways (either orange or pink).- We can select any one of the uncoloured faces adjacent to the silver face in 2 ways.- We can select any one of the remaining uncoloured faces in 2 ways.Total number of cubes satisfying the given conditions = 2 * 2 * 2 = 8Hence, the correct option is (

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines, isa)6b)18c)12d)9Correct answer is option 'B'. Can you explain this answer?
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