# find the number of ways in which the 6 petals of a white flower is painted with 6 different colours

### Mohammed

Guys, does anyone know the answer?

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

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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

Medium Open in App Solution Verified by Toppr

Correct option is A)

Number of sides of a cube =6Number 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

= 4×6 6! =5×3×2 =30 Ways

Hence, the correct answer is 30 Ways.

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## In how many ways can I colour the six faces of a cube with six different colours?

Answer (1 of 14): This is a bit complicated so pay attention. First we will find the total number of ways by which 6 different colors can paint a cube. This turns out to be 6! (i.e. you have 6 choices for 1st face, 5 choices for 2nd, 4 choices for 3rd and so on). But this cannot be our final ans...

In how many ways can I colour the six faces of a cube with six different colours?

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Sort Rishabh Varma

Comfortable with Concepts of MathematicsAuthor has 112 answers and 677.8K answer views5y

This is a bit complicated so pay attention.

First we will find the total number of ways by which 6 different colors can paint a cube. This turns out to be 6! (i.e. you have 6 choices for 1st face, 5 choices for 2nd, 4 choices for 3rd and so on). But this cannot be our final answer as this particular solution will Demands from us that we be able to distinguish between 6 identical sides of a cube when it is rotated. THIS is not possible.

Now what we need to do is to Fix cube so that repetition is prevented and the concern regarding identifying the sides becomes irrelevant. For this consider the Cu

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Madhusudhana Rao Sankarapu

Director (Business Development) at Kenra Technologies LLP, Secunderabad (2017–present)Author has 575 answers and 877.5K answer views4y

Let us consider that six faces of cube are denoted as FOUR sides, one top side and one bottom side. Let us paint the top side with blue color. There are other five faces remaining for painting. The opposite face of blue colored face i.e., bottom side to be colored next and it can be done in 5 ways.

The remaining 4 side faces form a circular permutation, these 4 faces can be colored in (4-1)! ways. It means 3! ways.

Hence, the total ways ways of painting a cube is equal to 5 x 3! = 5 x 6 = 30 ways

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Lakshya Jain

Loves MathAuthor has 343 answers and 1.9M answer views7y

Consider the face that has red color. There are five faces remaining. The face that is exactly opposite to the red face can be colored in 5 ways. The remaining 4 faces form a circular permutation, that can be colored in (4-1)! ways.

So total ways = 5∗3!=30 5∗3!=30 Shef

Love to play with numbers6y

Let's say that 6 different colors are c1, c2, c3.. c6.

Now let's consider that the face of cube facing up is painted with c1. Then the face of cube at the bottom can be painted in 5 different ways.

And the 4 faces on the horizontal side are in circular permutation so they can be painted in (4–1)! ways

So total number of ways cube can be painted

= 5* (4–1)! = 5*3! = 5*3*2 = 30 ways

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Gokul Nair

Studied at Christ Nagar Higher Secondary School4y

Let’s first solve the simplified version of this question by not taking the ‘cube’ aspect into it.

6 faces

f1, f2, f3, f4, f5, f6

each can be colored 6 different ways, but once we’ve used one color, we cant use it again- so that makes in 6*5*4*3*2*1 (6!) ways

So, total possible combinations are 6!

Now lets consider the complication: 6! possibilities are for when f1 is at position 1 (shown in image), f2 is at position 2.. and so on. But the cube of a particular color combination can be moved such that face1 comes at position 1,2,3,4,5 and 6 but it remains the same cube.

We should also note that even

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Dave Carlson

Studied Mechanical Engineering at University of Minnesota - Twin CitiesAuthor has 367 answers and 489.1K answer views5y

Related

If each face of a cube is coloured with one of 6 different colours, how many ways can it be done?

Do you mean that every side must be a different color?

Let’s say your colors are: Red, Orange, Yellow, Green, Blue, Purple

You can start by painting any side red, since one of them has to be. Then rotate that side to face you.

Now to add orange - There are two options: either the side opposite red must be orange, or one of the adjacent sides must be orange.

If one of the adjacent sides is orange, then you can paint one of those orange, and rotate so it faces upwards (note that in doing this, you keep the red side facing you, so you aren’t changing the configuration of the colors). At this point, a

## The number of ways of painting the faces of a cube with six different colours is

The number of ways of painting the faces of a cube with six different colours is

The number of ways of painting the faces of a cube with six different colours is

Updated On: 27-06-2022

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Guys, does anyone know the answer?