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From the letters in MAGOOSH, we are going to make three-letter "words.
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12 Nov 2019, 02:37
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50% (02:10) correct 50% (02:14) wrong based on 18 sessions
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From the letters in MAGOOSH, we are going to make three-letter "words." Any set of three letters counts as a word, and different arrangements of the same three letters (such as "MAG" and "AGM") count as different words. How many different three-letter words can be made from the seven letters in MAGOOSH?
From the letters in MAGOOSH, we are going to make three-letter "words.
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12 Nov 2019, 07:12
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hudacse6 wrote:
From the letters in MAGOOSH, we are going to make three-letter "words." Any set of three letters counts as a word, and different arrangements of the same three letters (such as "MAG" and "AGM") count as different words. How many different three-letter words can be made from the seven letters in MAGOOSH?
A. 135 B. 170 C. 123 D. 121 E. 720
(I) Take all different letters.. M, A, G, O, S and H, so 6 letters... They can be arranged in 6*5*4=120 ways (II) two are O and third any of remaining 5.. So \(5*\frac{3!}{2!} =15\) as each combination can be arranged in \(\frac{ 3!}{2!}\) ways
From the letters in MAGOOSH, we are going to make three-letter "words.
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12 Nov 2019, 09:02
chetan2u wrote:
hudacse6 wrote:
From the letters in MAGOOSH, we are going to make three-letter "words." Any set of three letters counts as a word, and different arrangements of the same three letters (such as "MAG" and "AGM") count as different words. How many different three-letter words can be made from the seven letters in MAGOOSH?
A. 135 B. 170 C. 123 D. 121 E. 720
(I) Take all different letters.. M, A, G, O, S and H, so 6 letters... They can be arranged in 6*5*3=120 ways (II) two are O and third any of remaining 5.. So \(5*\frac{3!}{2!} =15\) as each combination can be arranged in \(\frac{ 3!}{2!}\) ways
Total 120+15=135
A
I am confused a bit. why we can't consider 7 letters from the beginning and arrange them? I mean 7*6*5 = 210?
Re: From the letters in MAGOOSH, we are going to make three-letter "words.
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12 Nov 2019, 09:18
1
merimanukyan wrote:
chetan2u wrote:
hudacse6 wrote:
From the letters in MAGOOSH, we are going to make three-letter "words." Any set of three letters counts as a word, and different arrangements of the same three letters (such as "MAG" and "AGM") count as different words. How many different three-letter words can be made from the seven letters in MAGOOSH?
A. 135 B. 170 C. 123 D. 121 E. 720
(I) Take all different letters.. M, A, G, O, S and H, so 6 letters... They can be arranged in 6*5*3=120 ways (II) two are O and third any of remaining 5.. So \(5*\frac{3!}{2!} =15\) as each combination can be arranged in \(\frac{ 3!}{2!}\) ways
Total 120+15=135
A
I am confused a bit. why we can't consider 7 letters from the beginning and arrange them? I mean 7*6*5 = 210?
If you take 7 letters it will consist of both O. Say the letters are M, A,G,O1,O2,S,H So these 7*6*5 will consist of O1MA and O2MA. But both are same, OMA, so there are repetition in 7*6*5.
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50% (02:10) correct 
