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# How many words can be formed by taking 4 letters at a time

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Senior Manager
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How many words can be formed by taking 4 letters at a time [#permalink]

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13 Jun 2005, 08:42
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How many words can be formed by taking 4 letters at a time of the letters of the word MATHEMATICS ?

A. 2448
B. 2450
C. 2451
D. 2452
E. 2454
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ash
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13 Jun 2005, 10:30
MATHEMATICS has 2Ms,2As,2Ts and HEICS

For four-letter words( ), the possiblities are

a) 2 same of one kind, 2 same of another kind
b) 2 same, 2 different
c) all 4 different

For a), we have to pick 2 out of the three repeaters and then arrange them. When you have 2 pairs of letters to be put in 4 spaces, all you need is the number of ways to select 2 spaces.

C(3,2)*C(4,2) = 18

For b), We have to pick 1 out of the three repeaters and 2 out of the remaining 7 and arrange them. To arrange a pair plus two unique things, we just need to pick 2 out of 4 spaces and note that the remaining two can switch places.

C(3,1)*C(7,2)*C(4,2)*2 = 3*21*6*2=756

For c), we just have to arrange 4 out of 8 unique letters.

P(8,4) = 1680

Total = 18+756+1680 = 2454

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Senior Manager
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13 Jun 2005, 20:11
OA is E.........2454
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ash
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13 Jun 2005, 22:40
good explanation AJB!

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13 Jun 2005, 22:40
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