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Permutation and combination Problems
by Saurabh Kumar - Sunday, 5 July 2009, 07:01 PM
  Q1.The Time Mock CAT test CATALYST 19 consists of four sections.Each section has a maximum of 45 marks. Find the number of ways in which a student can qualify in the AMS MOCK CAT if the qualifying marks is 90.(Source of question:Arun Sharma's book, chapter Permutation and Combination LOD-3 q.nO.50

Q2.There are 5 bottles of sherry and each have their respective caps.If you are asked to put the correct cap on correct bottle then how many ways are there so that not a single cap is on correct bottle.Plase solve the question by logic.
(Source of question :Arun Sharama's book , chapter Permutation and combination, LOD-3, q.no. 39)

Q3.Six white and six black balls of same size are distributed among the ten urnsso that there is at least one ball in each urn.What is the number of different distributions of the ball?((Source of question :Arun Sharama's book , chapter Permutation and combination, LOD-3, q.no. 32)

Q4.How many six digit numbers contain 4 different digits?(Source of question :Arun Sharama's book , chapter Permutation and combination, LOD-3, q.no. 30)



Q5.Seven different objects must be didvided among three people. In how many ways can be this done if one or two of them cn get no objects. (Source of question :Arun Sharama's book , chapter Permutation and combination, LOD-2, q.no. 44)
Re: Permutation and combination Problems
by kamal upadhyay - Monday, 6 July 2009, 03:06 PM
  Answer for 5 ques ==>15 ???
Answer for 2 ques==> 44 ???
Answer for  4 question==>(4X9x9x8x7x6) ???


 
Re: Permutation and combination Problems
by A. SINGH - Tuesday, 7 July 2009, 03:30 AM
 

hello ...

TG sir and othr TGites , plz help and solve these questions

 

Re: Permutation and combination Problems
by Saurabh Kumar - Tuesday, 7 July 2009, 09:12 AM
  @kamal

Answer for 5 and 4 are wrong. Answer for 2 is correct.Can u plz let me know how u solved Q no. 2.. I know the direct formula,,if you have solved through logic..plz let us know
Re: Permutation and combination Problems
by shashank jain - Tuesday, 7 July 2009, 09:42 AM
  5)  381

4)  154224   (9*9*8*7*34)
Re: Permutation and combination Problems
by kamal upadhyay - Tuesday, 7 July 2009, 03:44 PM
  Hey sorry for question 5 i read it wrongly.It says different object.I took it as identical object.
Ans 5-->37-->2187 ???
Re: Permutation and combination Problems
by kamal upadhyay - Tuesday, 7 July 2009, 04:13 PM
  Ans2-->It is like dearrangment
So suppose you have bottle with 5 caps you want to put in such a way that


D1-->only one cap is put on wrong bottle.-->0 (since 1 is on wrong then one other must also be on wrong).So we can never have only one cap on wrong bottle.
D2-->two on wrong-->1 ( like a b are two bottles and c d are their two caps repectively then wrong way is one only i.e a -c and b-d)
Note here i am talking about way.
D3-->2 (a-b-c--->p-q-r ----> a -q,b-r,c-p and a-r,b-p,c-q)
D4-->total ways - (all on right bottle)- (1 on right bottle)-(2 on right bottle)-(3 on right bottle)
D4=4!-1-4c1xD1-4c2xD2-4c3xD3
D4= 4!- 1-  4c1x0 -4c2x1-4c3x2=24-1-0-6-4x2=24-15=9
So D4 is 4 caps on wrong bottle.
D5=5!-1-5C1x0-5C2x1-5C3x2-5C4x9=120-1-0-10-20-45=120-76=44-->Ans

Re: Permutation and combination Problems
by Devil Devil - Sunday, 12 July 2009, 01:53 PM
  Q1. 180C90 (Assuming marks alloted to each ques = 1 and with no negative marking, else marks alloted to each ques and negative marks must be mentioned).
Q2. No. of ways= (total number of ways - 5 correct - 4 correct -3 correct -2 correct -1 correct)
Total no. of ways = 5!
5 correct = 1
4 correct = 0
3 correct = 5C3 X 1
2 correct = 5C2 X 2
1 correct = 5C1 X 9
Q3.One urn having 3 balls= 10C1 X 4
     Two urns having 2 balls=  10C2 X 2
Q4. 9*(6c4 X 9 X8 - 5c4 X 9 X 9) + 5C4 X 9 X9 = 6490
5. 37 ( each of object can be given to any person, as there is no limitation on number of objects received by a person).
 Correct me if I am wrong
Re: Permutation and combination Problems
by Pravin Mishra - Thursday, 27 March 2014, 04:46 PM
  @Saurabh,

what is direct formula for problem number 2?
Re: Permutation and combination Problems
by sharmeet kamboj - Sunday, 30 March 2014, 01:33 PM
  ans 4 15120
Re: Permutation and combination Problems
by sharmeet kamboj - Sunday, 30 March 2014, 01:35 PM
  can you provide the solution
Re: Permutation and combination Problems
by TG Team - Wednesday, 2 April 2014, 01:50 PM
 

Hi Sharmeet smile

#4. How many six digit numbers contain four different digits?

It is a bit lengthier one. I am just giving a hint for this.

Let the four different digits being used are a, b, c, d. So the six digit number formed could have digits: CASE - I - {a, a, a, b, c, d} or CASE - II - {a, a, b, b, c, d}.

Now further you need to take care of 'zero' in both cases that it cannot be used at first place.
I hope it is easier to calculate now. smile

Kamal Lohia 

 

 

 

Re: Permutation and combination Problems
by Dhwani Trivedi - Friday, 2 May 2014, 11:34 AM
  hello..shouldnt we use the derangement formula for Q2?
Re: Permutation and combination Problems
by TG Team - Tuesday, 13 May 2014, 01:18 PM
  That's correct Dhwani smile

It is derangement of 5 pairs only.

Kamal Lohia
Re: Permutation and combination Problems
by Ankit Kaushik - Thursday, 19 November 2015, 03:41 AM
  For the first one try this approach.

we have to find the ways which will make the sum of scores to b 90.Put it another way, we are looking for ways by which one loses 90 marks out of 180 to get net 90 marks.

so, that is way of finding solution for
a + b + c + d = 90 where 0