0

Guest

Courses New

Each off the faces of the cube is coloured by a different colour .How many of the colouringss are distinct?

Each off the faces of the cube is coloured by a different colour .How many of the colouringss are distinct?

Grade:10

1 Answers

Saurabh Kumar
askIITians Faculty 2411 Points
7 years ago


A cube can be rotated into 6×4=24 configurations (i.e. the red face can be any one of the 6, and then there are 4 ways to rotate it that keep that face red), so the number of different colourings (counting rotations, but not mirror reflections, as the same) is 6!/24=30.



Case n=6: Colour one side with the ugliest colour, and put the cube on a table ugly side down. There are 5 choices for the colour on top. For each of these choices, colour the side facing you with the nicest remaining colour. The last three sides can be coloured in 3! ways, so the number of colourings is (5)(3!).

Case n>6: First choose the colours, then use them. The number of colourings is(n6)(5)(3!).

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on 10 grade maths

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More