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The number of ways in which four faces of a regular tetrahedron can be painted with four different colours is
- a)2!
- b)4!
- c)1!
- d)3!
Correct answer is option 'C'. Can you explain this answer?
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Solution:
A regular tetrahedron has 4 faces.
Therefore, we can paint each face in 4 different colours.
To find the number of ways in which we can paint 4 faces with 4 different colours, we can simply use the multiplication rule of counting.
Using the multiplication rule, the total number of ways in which we can paint the 4 faces is:
4 x 3 x 2 x 1 = 24
However, we need to remember that a regular tetrahedron is symmetric. This means that any two paint jobs that are the same when the tetrahedron is rotated are considered the same.
There are 4 rotational symmetries of a regular tetrahedron. They are:
- The identity rotation (no rotation)
- A rotation of 120 degrees about an axis passing through a vertex and the center of the opposite face
- A rotation of 240 degrees about an axis passing through a vertex and the center of the opposite face
- A rotation of 180 degrees about an axis passing through the midpoints of two opposite edges
Since there are only 4 rotational symmetries, and any two paint jobs that are the same when the tetrahedron is rotated are considered the same, we can divide the total number of ways by 4 to get the number of distinct paint jobs. This gives us:
24 / 4 = 6
Therefore, the number of ways in which four faces of a regular tetrahedron can be painted with four different colours is 1!, which is equal to 1.
A regular tetrahedron has 4 faces.
Therefore, we can paint each face in 4 different colours.
To find the number of ways in which we can paint 4 faces with 4 different colours, we can simply use the multiplication rule of counting.
Using the multiplication rule, the total number of ways in which we can paint the 4 faces is:
4 x 3 x 2 x 1 = 24
However, we need to remember that a regular tetrahedron is symmetric. This means that any two paint jobs that are the same when the tetrahedron is rotated are considered the same.
There are 4 rotational symmetries of a regular tetrahedron. They are:
- The identity rotation (no rotation)
- A rotation of 120 degrees about an axis passing through a vertex and the center of the opposite face
- A rotation of 240 degrees about an axis passing through a vertex and the center of the opposite face
- A rotation of 180 degrees about an axis passing through the midpoints of two opposite edges
Since there are only 4 rotational symmetries, and any two paint jobs that are the same when the tetrahedron is rotated are considered the same, we can divide the total number of ways by 4 to get the number of distinct paint jobs. This gives us:
24 / 4 = 6
Therefore, the number of ways in which four faces of a regular tetrahedron can be painted with four different colours is 1!, which is equal to 1.
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The number of ways in which four faces of a regular tetrahedron can be painted with four different colours isa)2!b)4!c)1!d)3!Correct answer is option 'C'. Can you explain this answer?
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The number of ways in which four faces of a regular tetrahedron can be painted with four different colours isa)2!b)4!c)1!d)3!Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of ways in which four faces of a regular tetrahedron can be painted with four different colours isa)2!b)4!c)1!d)3!Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways in which four faces of a regular tetrahedron can be painted with four different colours isa)2!b)4!c)1!d)3!Correct answer is option 'C'. Can you explain this answer?.
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