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# A 3-letters code consists of three different letters. If the code cont

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Manager
Joined: 29 Jul 2009
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A 3-letters code consists of three different letters. If the code cont  [#permalink]

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19 Feb 2010, 11:35
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A 3-letters code consists of three different letters. If the code contains at least 2 vowels, how many such codes are possible?
Manager
Joined: 22 Dec 2009
Posts: 249
Re: A 3-letters code consists of three different letters. If the code cont  [#permalink]

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19 Feb 2010, 13:28
apoorvasrivastva wrote:
A 3 -letters code consists of three different letters. If the code consists of at least 2 vowels.How many such codes are possible?

Dont have the OA

VVC + VVV

where V = Vowel
C = Consonant

VVC = 5c1 x 4c1 x 21c1 x 3! = 5x4x21x6= 2520

VVV = 5c1 x 4c1 x 3c1 x 3! = 5 x 4 x 3 x 6 = 360

VVC + VVV = 2880 (Ans)
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Manager
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Re: A 3-letters code consists of three different letters. If the code cont  [#permalink]

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19 Feb 2010, 14:03
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2 vowels and 1 consonant - can arrange in 3 ways VVC, VCV, CVV = 5 * 4 * 21 * 3 = 1260
3 vowels - VVV - 5 * 4 * 3 = 60

total = 1320
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Re: A 3-letters code consists of three different letters. If the code cont  [#permalink]

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19 Feb 2010, 14:14
chix475ntu wrote:
2 vowels and 1 consonant - can arrange in 3 ways VVC, VCV, CVV = 5 * 4 * 21 * 3 = 1260
3 vowels - VVV - 5 * 4 * 3 = 60

total = 1320

Its a code we are talking abt. Hence the arrangement between two vowels would also matter...

as per you have considered only VVC.... that means ... AEX ... and EAX is the same.... which is wrong! Please check.
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Re: A 3-letters code consists of three different letters. If the code cont  [#permalink]

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19 Feb 2010, 14:33
jeeteshsingh wrote:
chix475ntu wrote:
2 vowels and 1 consonant - can arrange in 3 ways VVC, VCV, CVV = 5 * 4 * 21 * 3 = 1260
3 vowels - VVV - 5 * 4 * 3 = 60

total = 1320

Its a code we are talking abt. Hence the arrangement between two vowels would also matter...

as per you have considered only VVC.... that means ... AEX ... and EAX is the same.... which is wrong! Please check.

we are already counting that in (5 * 4) ... for example ..
how many ways to select 2 out of a e i o u where order doesnt matter - 5 * 4 / 2 = 10 and the options are
ae, ai, ao, au, ei, eo, eu, io, iu, ou ... COMBINATIONS
if order matters than each one will have its counterpart .. example ae, ea .. and the number becomes 5 * 4 = 20 - PERMUTATIONS ..

you are taking permutations and then multipluing those again with 3! to get duplicates.
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Joined: 01 Feb 2010
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Re: A 3-letters code consists of three different letters. If the code cont  [#permalink]

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21 Feb 2010, 00:45
Answer is: (5C2. 21C1. 3!) + (5P3) or (5C2. 21C1. 3!) + (5C3 * 3!) == 1260 + 60= 1320.
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PNC: A-3 letters code consists of three different letters.  [#permalink]

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07 Dec 2014, 10:02
Hi,

Could someone please let me know strategy to solve following question. I do not have answer of it.

Question:

A 3-letters code consists of three different letters. If the code contains at least 2 vowels, how many such codes are possible.

Regards,
Ammu
Senior Manager
Joined: 13 Jun 2013
Posts: 266
Re: PNC: A-3 letters code consists of three different letters.  [#permalink]

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07 Dec 2014, 11:10
ammuseeru wrote:
Hi,

Could someone please let me know strategy to solve following question. I do not have answer of it.

Question:

A 3-letters code consists of three different letters. If the code contains at least 2 vowels, how many such codes are possible.

Regards,
Ammu

following 2 cases are possible.

case 1: code contains 2 vowels and 1 consonant= 5C2.21C1 (5= total no. of vowels, 21= total no. of consonants)

case 2: code contains 3 vowels. = 5C3

thus total number of codes = 5C2.21C1 + 5C3= 210+10 = 220
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Re: PNC: A-3 letters code consists of three different letters.  [#permalink]

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08 Dec 2014, 01:34
manpreetsingh86 wrote:
ammuseeru wrote:
Hi,

Could someone please let me know strategy to solve following question. I do not have answer of it.

Question:

A 3-letters code consists of three different letters. If the code contains at least 2 vowels, how many such codes are possible.

Regards,
Ammu

following 2 cases are possible.

case 1: code contains 2 vowels and 1 consonant= 5C2.21C1 (5= total no. of vowels, 21= total no. of consonants)

case 2: code contains 3 vowels. = 5C3

thus total number of codes = 5C2.21C1 + 5C3= 210+10 = 220

Hi,

You will have to multiply 220 by 3!. You have taken into account only selection of letters and not their arrangement.
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Joined: 13 Jun 2013
Posts: 266
Re: PNC: A-3 letters code consists of three different letters.  [#permalink]

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08 Dec 2014, 02:53
desaichinmay22 wrote:
manpreetsingh86 wrote:
ammuseeru wrote:
Hi,

Could someone please let me know strategy to solve following question. I do not have answer of it.

Question:

A 3-letters code consists of three different letters. If the code contains at least 2 vowels, how many such codes are possible.

Regards,
Ammu

following 2 cases are possible.

case 1: code contains 2 vowels and 1 consonant= 5C2.21C1 (5= total no. of vowels, 21= total no. of consonants)

case 2: code contains 3 vowels. = 5C3

thus total number of codes = 5C2.21C1 + 5C3= 210+10 = 220

Hi,

You will have to multiply 220 by 3!. You have taken into account only selection of letters and not their arrangement.

yes, i forgot to multiply 220 with 3!.
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Posts: 58407
Re: A 3-letters code consists of three different letters. If the code cont  [#permalink]

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08 Dec 2014, 04:10
apoorvasrivastva wrote:
A 3-letters code consists of three different letters. If the code contains at least 2 vowels, how many such codes are possible?

Merging similar topics. Please refer to the discussion above and ask if anything remains unclear.

Check Constructing Numbers, Codes and Passwords in our Special Questions Directory.

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Re: A 3-letters code consists of three different letters. If the code cont  [#permalink]

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18 Dec 2015, 12:08
5 Vowels
21 Consonants

Remember that the letters have to different.

At least 2 = 2-Vowels + 3-Vowels
2-Vowels: 5*4*21 = 420
3-Vowels: 5*4*3 = 60

Total = 480
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Re: A 3-letters code consists of three different letters. If the code cont  [#permalink]

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30 Jan 2019, 09:22
We have 5 vowels (A,E,I,O,U) and 21 consonants.

Restriction 1: must have 3 different letters
Restriction 2: must have at least 2 vowels

Case 1: 3 vowels = 5*4*3 = 60 possibilities
Case 2: 2 vowels, 1 consonant = 5*4*21 *3(for the position of the consonant)

Re: A 3-letters code consists of three different letters. If the code cont   [#permalink] 30 Jan 2019, 09:22
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