Perms and combs q
How many permutations of the letters DANIEL do not begin with D or do not end with L?
I would have thought it was 6!, minus the 5! with D at the front with 5! with L at the end - then minus the perms with D and L together (which is counted twice.
ie 6!-(2x5!)-4!
So my answer is 456, but the book answer says 696, which seem quite high.
Any ideas?
I would have thought it was 6!, minus the 5! with D at the front with 5! with L at the end - then minus the perms with D and L together (which is counted twice.
ie 6!-(2x5!)-4!
So my answer is 456, but the book answer says 696, which seem quite high.
Any ideas?
Original post by Gmart
How many permutations of the letters DANIEL do not begin with D or do not end with L?
I would have thought it was 6!, minus the 5! with D at the front with 5! with L at the end - then minus the perms with D and L together (which is counted twice.
ie 6!-(2x5!)-4!
So my answer is 456, but the book answer says 696, which seem quite high.
Any ideas?
I would have thought it was 6!, minus the 5! with D at the front with 5! with L at the end - then minus the perms with D and L together (which is counted twice.
ie 6!-(2x5!)-4!
So my answer is 456, but the book answer says 696, which seem quite high.
Any ideas?
Is that the exact question?
They have just subtracted the 4!
Original post by TenOfThem
Is that the exact question?
They have just subtracted the 4!
They have just subtracted the 4!
It is the exact question - I am surprised that they did that, surely that just takes out the combs with both D and L at the beginning/end??? leaving a reasonable number without D at the beginning or L at the end. Very confusing wording...
Maybe it is to do with de morgans, when it says 'or' it means 'and'?
Original post by Gmart
Surely the 'or' refers to the union of the sets rather than the intersection...
To be honest, I think it is a badly phrased question
Everything is correct in the question yet it could be quite hard to understand that.
A - situation in which D is not the first letter
B - situation in which L is not the last letter
|A|=5x5!=600 -> we are choosing one out of five places for letter D (cannot be the first place, therefore 5) and then we are choosing places for the remaining letters
|B|=5x5!=600 -> we are choosing one out of five places for letter L (cannot be the last place, therefore 5) and then we are choosing places for the remaing letters
|A∩B|=504 -> SEE THE ATTACHED PICTURE, THIS IS THE HARDEST PART
|AUB|=|A|+|B|-|A∩B| => |AUB|=600+600-504=696
Feel free to ask if you don't understand something
A - situation in which D is not the first letter
B - situation in which L is not the last letter
|A|=5x5!=600 -> we are choosing one out of five places for letter D (cannot be the first place, therefore 5) and then we are choosing places for the remaining letters
|B|=5x5!=600 -> we are choosing one out of five places for letter L (cannot be the last place, therefore 5) and then we are choosing places for the remaing letters
|A∩B|=504 -> SEE THE ATTACHED PICTURE, THIS IS THE HARDEST PART
|AUB|=|A|+|B|-|A∩B| => |AUB|=600+600-504=696
Feel free to ask if you don't understand something
(edited 9 years ago)
Original post by Gmart
How many permutations of the letters DANIEL do not begin with D or do not end with L?
'do not begin with D or do not end with L' statement is the negation of the
original one, which would be
'.. begin with D AND end with L' (De Morgan) -> 4!
So You have to subtract only this number of permutations from the 6!
(edited 9 years ago)
Original post by eloo
Everything is correct in the question yet it could be quite hard to understand that.
A - situation in which D is not the first letter
B - situation in which L is not the last letter
A - situation in which D is not the first letter
B - situation in which L is not the last letter
A and B are not simple statements because the red NOT is a logical operator
You should state
A - situation in which D is the first letter
B - situation in which L is the first letter
E - all permutation
So the complete statement in the question is
Unparseable latex formula:
\displaystyle \neg A \lor \neg B \right = \neg \left (A \land B \right )
So the question is (P = permutation)
(edited 9 years ago)
Original post by ztibor
A and B are not simple statements because the red NOT is a logical operator
You should state
A - situation in which D is the first letter
B - situation in which L is the first letter
E - all permutation
So the complete statement in the question is
So the question is (P = permutation)
You should state
A - situation in which D is the first letter
B - situation in which L is the first letter
E - all permutation
So the complete statement in the question is
Unparseable latex formula:
\displaystyle \neg A \lor \neg B \right = \neg \left (A \land B \right )
So the question is (P = permutation)
Not quite sure if I clearly understand that but isn't it the same? I simply changed the way I described both A and B and in it's effect I counted situation in which either A or B happens - as in the question. So my (AUB) is when L is not the last letter OR D is not the first letter OR both.
Posted from TSR Mobile
Quick Reply
Related discussions
- Grade 99 Combined Science resources (Edexcel) GCSE
- how to clean air conditioner coils
- Korean hair perm
- bf asmr
- Combination and Permutation Question
- My friend keeps giving me headlice
- Options
- Make it More Barber-ey !!
- GCSE AQA Computer Science resources
- Hello there!
- Surfaces and textures art gcse mock
- Cognito
- Cyberstart HQ level 6 challenge 8: Junya Who?
- about myself
- permutations Problem
- ucl kcl edinburgh
- How do I stop myself from worrying after year 13?
- Working in the civil service or APHA
- Grammatical mistake on PS
- QUB (Queens University Belfast) vs QMUL (Queen Mary University London) for medicine.
Latest
Trending
Last reply 3 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
Trending
Last reply 3 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
