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MATHEMATICS---> How many 4 letters word can be formed ?
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Re: 4 letter words [#permalink]
 21 May 2011, 00:25
there are 8 distinct letters in MATHEMATICS. They are MATHEICS. So, no 4 letter words from 8 letters= 8p4= 8!/4!=1680.
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Re: 4 letter words [#permalink]
21 May 2011, 00:27
jamifahad wrote: there are 8 distinct letters in MATHEMATICS.
They are MATHEICS.
So, no 4 letter words from 8 letters= 8p4= 8!/4!=1680. Why are you not considering repeating the same letters in the four letter?
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Re: 4 letter words [#permalink]
21 May 2011, 00:47
from 11 letters any 4 can be chosen here. 11*10*9*8
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Re: 4 letter words [#permalink]
21 May 2011, 00:52
amit2k9 wrote: from 11 letters any 4 can be chosen here.
11*10*9*8 Amit you have not taken care of repeated letters MM AA TT
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Re: 4 letter words [#permalink]
21 May 2011, 01:00
Repeating characters - total ways = 11 * 10 * 9 * 8 Non repeating characters - Total ways = 5C4 + 5C3 * 3 + 3C2 * 5C3 + 1* 5C1 Whats the OA? hussi9 wrote: MATHEMATICS---> How many 4 letters word can be formed ?
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Re: 4 letter words [#permalink]
21 May 2011, 01:13
hussi9 wrote: amit2k9 wrote: from 11 letters any 4 can be chosen here.
11*10*9*8 Amit you have not taken care of repeated letters MM AA TT Then i think 8*8*8*8 different ways. to arrange 4 letters. What am i missing?
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Re: 4 letter words [#permalink]
21 May 2011, 02:20
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hussi9 wrote: MATHEMATICS---> How many 4 letters word can be formed ? 2 M , 2 A and 2 T. Total words that can be formed. 11!/(2!)^3 Total 4 letter words, 11P4 4 letter distinct words that can be formed( MATHEICS) 8P4 2 same 2 distinct 1 pair from ( M,A,T) in 3C1 ways rest 7C2 *4!2! so its 3C1*7C2*4!/2! 2 same of one kind and 2 same of other kind. 3C2*4!/(2!)^2
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Re: 4 letter words [#permalink]
21 May 2011, 06:52
2 M, 2 A, 2 T,1 H, 1 E, 1 I, 1 C, 1 S So Total # (assuming repitition) = 8^4
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Re: 4 letter words [#permalink]
21 May 2011, 09:27
Please let us know the correct answer.
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Re: 4 letter words [#permalink]
24 May 2011, 12:02
1. Let us first consider the UNIQUE letters in the word MATHEMATICS
M, A, T, H, E, I, C, S
Number of ways 4 letter word can be formed = 8P4 = 1680 ways
2. Let us now consider the DUPLICATE letters in the given word
M, M , A, A, T, T
Number of ways 4 letter word can be formed = 6P4 /2!2!2! = 60 ways
Therefore total number of ways = 1680 + 60 = 1740 ways
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Re: 4 letter words [#permalink]
25 May 2011, 04:13
sudhir18n wrote: hussi9 wrote: MATHEMATICS---> How many 4 letters word can be formed ? 2 M , 2 A and 2 T. Total words that can be formed. 11!/(2!)^3 Total 4 letter words, 11P4 4 letter distinct words that can be formed( MATHEICS) 8P4 2 same 2 distinct 1 pair from ( M,A,T) in 3C1 ways rest 7C2 *4!2! so its 3C1*7C2*4!/2! 2 same of one kind and 2 same of other kind. 3C2*4!/(2!)^2 This approach is corect
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Re: 4 letter words
[#permalink]
25 May 2011, 04:13
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