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# How many different flags can be made from4 colors- Red, Blue, Green, a

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Joined: 04 Jan 2015
Posts: 2577
How many different flags can be made from4 colors- Red, Blue, Green, a  [#permalink]

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Updated on: 13 Aug 2018, 06:08
00:00

Difficulty:

85% (hard)

Question Stats:

39% (02:02) correct 61% (01:36) wrong based on 102 sessions

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Fool-proof method to Differentiate between Permutation & Combination Questions - Exercise Question #3

How many different flags can be made from4 colors- Red, Blue, Green, and White such that no color is repeated more than once?

Options:
A. 25
B. 24
C. 48
D. 60
E. 64

Learn to use the Keyword Approach in Solving PnC question from the following article:

Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions

Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions

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Originally posted by EgmatQuantExpert on 11 Apr 2018, 22:16.
Last edited by EgmatQuantExpert on 13 Aug 2018, 06:08, edited 6 times in total.
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Re: How many different flags can be made from4 colors- Red, Blue, Green, a  [#permalink]

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11 Apr 2018, 22:44
1
EgmatQuantExpert wrote:
Learn the structured approach to identify permutation and combination question - Exercise Question #2

How many different flags can be made from4 colors- Red, Blue, Green, and White?

Options:
A. 25
B. 24
C. 48
D. 60
E. 64

There are 4 different colors which can be used to make the flags.

When there is 1 color in the flag - 4 possibilities
When there are 2 colors in the flag - 4*3 = 12 possibilities
When there are 3 colors in the flag - 4*3*2 = 24 possibilities
When there are 4 colors in the flag - 4*3*2*1 = 24 possibilities

Therefore, there are a total of 4+12+24+24 = 64 possibilities(Option E) in which the flags can be made.
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Joined: 02 Aug 2009
Posts: 7334
Re: How many different flags can be made from4 colors- Red, Blue, Green, a  [#permalink]

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11 Apr 2018, 23:53
EgmatQuantExpert wrote:
Learn structured approach to identify permutation and combination question - Exercise Question #2

How many different flags can be made from4 colors- Red, Blue, Green, and White?

Options:
A. 25
B. 24
C. 48
D. 60
E. 64

The question is incomplete the way it is..

1) I would say - " different flags from 20 m cloth if one flag is .....", so it should be different types of flags..
I am sure it means this so we can leave it here..
2) If I use two colors also, I can make 100s of different types of flags..

so the question could have been two ways..

A) "How many different types of flags can be made from using atleast one of 4 colors- Red, Blue, Green, and White" - Without any restrictions
so a COMBINATION question..
one colour - 4 ways
two colours - 4C2 - 6 ways
three colour - 4C3 - 6 ways
four colour - 4C4 - 1 way

total = 17 ways

B) "How many different types of flags can be made from using atleast one of 4 colors - Red, Blue, Green, and White -in horizontal stripe/vertical stripes, each coloured being used once" - With restrictions
so a PERMUTATION question..
one colour - 4 ways
two colours - 4P2 - 6*2=12 ways
three colour - 4P3 - 6*3!=24 ways
four colour - 4P4 - 4*3*2*1=24 way

total = 64 ways
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Posts: 2577
Re: How many different flags can be made from4 colors- Red, Blue, Green, a  [#permalink]

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17 Apr 2018, 07:51

Solution

Given:
• We have 4 colours- Red, Blue, Green, and White to form the flag.

To find:
• The number of ways we can form different flags from the 4 colours available.

Approach and Working:

• From the 4 colors available, we can form 4 different types of flag:
o Flag with single color
o Flag with two colors
o Flag with three colors
o Flag with four colors

• Hence, total number of flags= Flag with one color +Flag with two colors + Flag with three colors+ Flag with four colors

Flag with one color:

From 4 colors, we can select 1 color to form the flag in $$^4c_1$$=4 ways.

Flag with more than one colors:

Since the order of colour matters in a flag, this is a case of permutation.
• Thus, total number of flags with two colours= $$^4P_2$$=2
• In the similar fashion, total number of flags with three colours and four colours = $$^4P_3$$= 24 and $$^4P_4$$=24 ways respectively.

Thus, total number of flags= 4+12+24+24= 64

Hence, option E is the correct answer.

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Joined: 04 Jan 2015
Posts: 2577
Re: How many different flags can be made from4 colors- Red, Blue, Green, a  [#permalink]

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17 Apr 2018, 08:06
Hey chetan2u,

Apology for the inconvenience.

We have updated the question.

Regards
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Re: How many different flags can be made from4 colors- Red, Blue, Green, a   [#permalink] 17 Apr 2018, 08:06
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