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

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

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

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New post 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 :(

my answer is 1320..please confirm if its is correct !!


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

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

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New post 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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New post 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
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Re: PNC: A-3 letters code consists of three different letters.  [#permalink]

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New post 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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New post 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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Re: PNC: A-3 letters code consists of three different letters.  [#permalink]

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

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New post 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?


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

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New post 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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New post 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)

Add together: 60+1260 = 1320
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Re: A 3-letters code consists of three different letters. If the code cont   [#permalink] 30 Jan 2019, 09:22
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