Rank of words (1 Viewer)

[juantheron]

1) The Letter of the word "ZENITH" are written in all possible orders. How many words are possible if all these written out as a Dictonary
What is the rank of the word "ZENITH"

2) The Letter of the word "SURITI" are written in all possible orders. How many words are possible if all these written out as a Dictonary
What is the rank of the word "SURITI"

plz explain me briefly I have no Idea How to tackle it

Thanks

 

[RealiseNothing]

What does it mean by rank?

 

[someth1ng]

What does it mean by rank?

First word in the dictionary is rank 1, the second word in the dictionary is rank 2...etc.

 

[iBibah]

What does it mean by rank?

When put in alphabetical order, what rank is it.

 

[RealiseNothing]

I'm going to assume you have to use all 6 letters?

Well consider the word ZENITH:

There are 6 distinct letters, so the amount of words you can make is 6!, ie there are 720 words in this dictionary.

Now let's consider how many words come after ZENITH:

Well since Z is the last letter of the alphabet, we can fix that in the first spot:

Z _ _ _ _ _

Now E is the 2nd letter. All the other 4 letters come after E in the alphabet, so we can have 4x4! words by putting the 2nd letter as either N, I, T, or H. Hence now we can say that 96 words come after ZENITH.

Let's fix the E in the 2nd spot now:

Z E _ _ _ _

Consider the 3rd letter, only T comes after N, so there are 3! more words that come after ZENITH. Hence there is an extra 6 words, and 96 + 6 = 02 words after ZENITH so far.

Fix the N:

Z E N _ _ _

Consider the 4th letter, only the T comes after the I, so there are 2! more words. 102 + 2 = 104.

Fix the I:

Z E N I _ _

Now no letters come after the T, so there are no more possible words that come after ZENITH.

Hence there are 104 words that come after ZENITH in the dictionary we made. Since there are 720 words in total, the rank of ZENITH must be 616.

 

[jackerino]

1) The Letter of the word "ZENITH" are written in all possible orders. How many words are possible if all these written out as a Dictonary
What is the rank of the word "ZENITH"

2) The Letter of the word "SURITI" are written in all possible orders. How many words are possible if all these written out as a Dictonary
What is the rank of the word "SURITI"

plz explain me briefly I have no Idea How to tackle it

Thanks

The word ZENITH could be rank 1 for all we know, but putting the dictionary restriction makes it more complex than that. So simply find alphabetical order of letters in their permutations


aaand realise gives the answer lolz

 

[Beaconite]

I suck at Perms Combs , hope it is not in the exam

 

[RealiseNothing]

Alternatively if you notice one thing you can do it much quicker.

There are 720 words in total, and since this starts with the last letter of the alphabet, it must be in the bottom 120 in ranks. Hence it is between 600 and 720.

Now we notice the 2nd letter is E, and no other letter comes before it in the alphabet, so if we find how many words appear before ZENITH in our dictionary that start with the letter Z, we can add that amount of to 600 to get the rank of ZENITH.

Fix Z and E:

Z E _ _ _ _

Now I and H come before N, so there are 2 x 3! words that precede ZENITH, hence there are 12 words so far.

Fix the N:

Z E N _ _ _

Only the H precedes I now, so there is 2! more words before ZENITH, hence in total there are 12 + 2! = 16 words that come before ZENITH.

Therefore 600 + 16 = 616, ZENITH is ranked 616.

 

[jackerino]

I suck at Perms Combs , hope it is not in the exam

its ALWAYS in the exam. Im pretty sure every single HSC paper has had at least 1 perm/comb question in it.

 

[Beaconite]

its ALWAYS in the exam. Im pretty sure every single HSC paper has had at least 1 perm/comb question in it.

I hate the hard ones, i can do simple ones and no, not every single exam has perm combs in it

 

[theind1996]

I hate the hard ones, i can do simple ones and no, not every single exam has perm combs in it

It almost always does though - you can't afford not to understand the topic well.

 

[Beaconite]

It almost always does though - you can't afford not to understand the topic well.

I HATE the topic, I never try to understand :!

 

[Leffife]

Permutations & Combinations can be quite tricky at times. I cannot say I'm superb with it, however, I don't really find it that difficult. I think for some reason my actual weakness is mathematical induction (almost every question) and circle geometry (only the top end questions). That is definitely something I need to work on.

 

[Beaconite]

Permutations & Combinations can be quite tricky at times. I cannot say I'm superb with it, however, I don't really find it that difficult. I think for some reason my actual weakness is mathematical induction (almost every question) and circle geometry (only the top end questions). That is definitely something I need to work on.

lol everyone has their own strengths and weaknesses, lol I am pre good at induction

 

[RealiseNothing]

My weaknesses are angles between two curves and ratio division of a line.

How does this even work.

 

[Beaconite]

My weaknesses are angles between two curves and ratio division of a line.

How does this even work.

Ur kidding right? LOL

 

[RealiseNothing]

Ur kidding right? LOL

Sadly not.

 

[Leffife]

My weaknesses are angles between two curves and ratio division of a line.

How does this even work.

Oh man yeah, that's now hard. Just makes no sense to me. Like how do you find the angle between two curves if we cannot use a protractor and also it's not drawn to scale...?
Ratio division of a line, forget it mate... no idea.

 

[Beaconite]

Oh man yeah, that's now hard. Just makes no sense to me. Like how do you find the angle between two curves if we cannot use a protractor and also it's not drawn to scale...?
Ratio division of a line, forget it mate... no idea.

do youse mean its hard to 'calculate' the angle ? :O

 

[juantheron]

Thanks friends Got it