Permutation & Combination problem

[raviagni]

I have a few questions on permutation and combination..

1)How many ways can the letters of the word 'computer' be arranged so that vowels occupy the even positions?

It will be great if someone tells the way also how to solve it,rather than giving only the answer

2)In how many ways can you put 9 coins of different values into 2 pockets

3)In a railway compartment,there are 2 rows of seats facing eac other with accommodation for 5 in each,4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?

Also tell me about problem 3 whether it's permutation or combination problem?

regards,
Ravi Agnihotri

[raviagni]

Would anyone care to reply friends????????

[Obsessed_bout_mba]

Originally Posted by raviagni

Would anyone care to reply friends????????

buddy

please go to the quants section and there will be a thread for permutation and combination..post ur query n that thread
plz dont start new threads for a single question when theres already a thread for it

i m not that good in permu combi..so i m not able to solve ur prob immediately except for the first one...plz post it in permu-combi forum in quants section or any other general discussion forum in quants section.

[prem_ravi]

Originally Posted by raviagni

I have a few questions on permutation and combination..

1)How many ways can the letters of the word 'computer' be arranged so that vowels occupy the even positions?

It will be great if someone tells the way also how to solve it,rather than giving only the answer

2)In how many ways can you put 9 coins of different values into 2 pockets

3)In a railway compartment,there are 2 rows of seats facing eac other with accommodation for 5 in each,4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?

Also tell me about problem 3 whether it's permutation or combination problem?

regards,
Ravi Agnihotri

Thanks Obsessed_abt_MBA...Yup, u have to post the same in the QA sections...

Anyways these are the answers.....

1.Look at the word Computer...u have 3 Vowels & 5 consonants...If Vowels have to occupy even places, it has to occupy position 2,4 ,6 or 8..Consonants have to occupy 1,3,5 &7...So, threee places have to be selected among the 4 even places i.e 4c3 or 4 ways, the vowels can occupy in 3! ways ie the position 2 by any of the 3 Vowels, position 4 by any one of the remaining 2 & the last one is default amongest the 3 selected places...Likewise consonants has to occupy in 5! ways...so the total arrangements would be4* 3! * 5! ways or 4*6 * 120 ways or 2880 ways...

2.lets look qtn 2 as 2 cases (since we are not sure whether the pockets look alike or different)

Now lets assume the coins to have the values from Rs.1 to Rs.9 ie 1,2,3,4,5,6,7,8,9

Case 1: Pocket 1 & 2 look different

Pocket 1 can hold as many as 0 coin to 9 coins

Pocket 1 to hold 0 coins = 1 way (now its the same for Pocket 2)

Now Pocket 1 to hold one coin it has 9 ways (2 pocket default it will have remaining 8 coins)..Same applies to Pocket 2 to have 1 coin & Pocket 1 to hold rest of the coins...

So total 9+9 = 18 coins

Pocket 1 to hold 2 coins..we have to find no of combinations ie 9c2 = 36 ways...Same for Pocket 2

So total 36+36 = 72

Now for 3 coins = 9c3 = 84+84 ways & soon....

till coins..

Case 2 if Pockets look same then divide the total by 2

3.its both (P&C)....

Now when out of 10 say ABCD out of ABCDEFGHIJ have decided to sit forward & EFG have decided to sit rear..it means their directions are fixed..Now out of the remaining 3, I have to choose 1 guy who would sit forward or 2 guys who would sit rear..This is = 3c1 or 3c2 = 3 ways...Now the directions are fixed...In the forward direction ABCD & the 5 the guy can sit in any order..so the arrangements would be 5*4*3*2*1=5!=120..Same applies to rear side = 120..Total ways=3*120*120=360*120=43200 ways.....

Correct me if Iam wong..Please dont open up threads ..Instead use the search option..Thank you & All the Best.......

Meanwhile I hope the Mod has closed one of the threads with same topic opened up by you..Please dont do this again as u may be barred from using for the reason of defying the rules...Please do look into the newbie guidelines

[made_for_iims]

1.
there are 5 consonants n 3 vowels...
out of which all vowels will be at even places
so out of 5, one consonant will be at even places...

choosin that consonant = 5
placin 3 vowels at four places = 4*3*2 = 24
placing 4 consonants at 4 places = 4*3*2*1 = 24

so total ways = 24*24*5 = 2880


2.
say one pocket is zero
other pocket is one...

so any coin can be in zero or one.... that makes two possible states...
hence total ways = 2^9.....
as prem said... if two pockets r considerd to be similar
2^9 / 2 = 2^8

3. i agree with prem's answer

[rmbt]

@Raviagni..........Refrain from opening multiple threads on the same topic.

Please use the SEARCH to locate the relevant threads. There is a separate section for quant.

Continue on this one:

http://www.pagalguy.com/forum/quanti...nation-67.html (doubts in permutation & combination)

All the best.