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13 Jun 2005, 08:42
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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
A. 2448
B. 2450
C. 2451
D. 2452
E. 2454
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13 Jun 2005, 10:30
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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
E is the answer
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
E is the answer
