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UPSC Civil Services 2019 Prelims General Studies Paper II
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© examsnet.com
Question : 5
Total: 80
Each face of a cube can be painted in black or white colours.
In how many different ways can the cube be painted?
9
10
11
12
Validate
Solution:
A cube has 6 symmetric faces.
Number of faces of a cube coloured by:
Black
White
Number of way
0
6
1
1
5
1
2
4
2 (two adjacent or two opposite faces are black)
3
3
2 (around a corner or not around a corner are either black or white)
4
2
2 (adjacent or opposite faces are white)
5
1
1
6
0
1
Hence, total number of ways
= 1 + 1 + 2 + 2 + 2 + 1 + 1 = 10
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