Question

The number of ways of painting the faces of a cube with $6$ different colors

• A. $30$
• B. $6$
• C. $6!$
• D. None of these

Answer 1

Answer: (A)

$30$

Number of sides of a cube $=6$

Number of colour of a cube $=6$

Number of ways of colouring $=?$

Concider a cube in $3D$ space

Each of the sides towards East West North South and remaning two up and down

Now fixing up positions down is also fixed

Total number of ways

$=\frac{6!}{4\times 6}=5\times 3\times 2$

$=30$ Ways

Hence, the correct answer is $30$ Ways.