Permutations & Combinations - Questions & Discussions

MBA CAT 2022
390
sprihharsh Says
5 students out of total of 3 students each from 3 different states are to be chosen for national integration camp.If each state is to have at least one representation,in how many ways van the selection be made?


is it 108

when 3,1,1=*3=27
when 2,2,1=*3=81

total=27+81=108
391

yes yes yes,it is 108....
But can you please elaborate the answer,i mean each step wise...

392

I guess I got the answer.
But thank you so much:D

393
yes yes yes,it is 108....
But can you please elaborate the answer,i mean each step wise...


take 1st case when 3 from one state and 1,1 from other states

we can select 3 from one state in 3c3 ways

and 1 in 3c1 ways,so it will become 3c3*3c1*3c1*3(3,1,1 this can permute in 3 ways like 3!/2!=3)=27

same for 2nd case:when we have taken 2,2,1

this can be done in 3c2*3c2*3c1*3(same reason why 3)=81
394

India and pakistan play a series of 7 one-day matches.Each match can be won,lost or drawn.If we are to forecast the results of these matches,then how many different forecasts will contain exactly 5 correct results

395
Is answer 7c5 X 2^2?
396

the answer is 7C2 x 2^2

397

find number of ways in which five students and 3 teachers can be arranged in a line such that no two teachers are together.

398
sprihharsh Says
the answer is 7C2 x 2^2


Yea it was a mis-print..
Expand (1+2)^7 and see the term with 2^2. i.e. the answer.
Here we have expanded 3^n , we have three options to do with 7 matches these are won, lost or drawn. n i s the number of matches. so 3^7 is the total number of possible cases.
out of which.. 7C2 X 2^2 is the required term.. :)
hope u got it..
399
sprihharsh Says
find number of ways in which five students and 3 teachers can be arranged in a line such that no two teachers are together.


Arrange 5 students like this
xSxSxSxSxSx S--> Students, x--> vacant space..

so for three teachers there are five places..
for the first there are 6 options, for next 5, for next 4..
so total ways..
6x5x4=120.
400

hey thankuuu so much,
I gt ur point...bt is there any other way of doing this question..
or can you explain it a little more,i mean some generalised concept..

401

yeah gt it...thankuuu so very much

402
hey thankuuu so much,
I gt ur point...bt is there any other way of doing this question..
or can you explain it a little more,i mean some generalised concept..


If you find binomial theorem approach difficult, you can try this:
You can select 5 matches out of 7 in 7C5 ways, whereas the wrong ones can be further arranged in 4 ways, say if the 6th and 7th match are won by India, you can predict, a (draw,draw),(loss,draw), (draw,loss), (loss,loss)

Therefore 7C2*4= 84
403

hmmm...okie
gt d point
thankuuuu:)

404
sprihharsh Says
5 students out of total of 3 students each from 3 different states are to be chosen for national integration camp.If each state is to have at least one representation,in how many ways van the selection be made?


hi puys!!
plz tell what's wrong in my approach...

First of all we can choose 3 people from each state:-3c1*3c1*3c1
the rest two can be from any state which can be choosen from rest 6 people in 6c2 ways...
so answer come out to be 3c1*3c1*3c1*6c2=27*15=405

plz explain where i m going wrong..:|
405

Hi,
A small confusion..
While arranging N letters to make different possible words ... what shall we assume, does it mean that we have to make N lettered words OR all possible words ?
Mentioning below questions for reference.

Q.1) How many words,with or without meaning,can be formed using ROCKET ?

Q.2) How many words, with or without meaning, without repetition, can be formed using TRIANGLE, where words should start with 'T' & end with 'E' ?

406
hi puys!!
plz tell what's wrong in my approach...

First of all we can choose 3 people from each state:-3c1*3c1*3c1

the rest two can be from any state which can be choosen from rest 6 people in 6c2 ways...
so answer come out to be 3c1*3c1*3c1*6c2=27*15=405

plz explain where i m going wrong..:|


As per my approach,
First of all we can choose 1 person from each state:-3c1*3c1*3c1 = 27

now it becomes a question of whole no. solution

a+b+c=2;

where a,b,c are the 3 states
2 student can be selected out of these 4C2= 6

hence total ways of selection= 27*6= 162.

Can someone explain the flaw in this approach..?? 😞
407

Hi Puys,

Can someone please explain the method for solving below problems!

1) No. of ways of distributing 'n' similar objects into 'r' similar groups.

2) No. of ways of distributing 'n' distinct objects into 'r' similar groups.

Thanks in adv.
Anupam

408
Hi,
A small confusion..
While arranging N letters to make different possible words ... what shall we assume, does it mean that we have to make N lettered words OR all possible words ?
Mentioning below questions for reference.

Q.1) How many words,with or without meaning,can be formed using ROCKET ?

Q.2) How many words, with or without meaning, without repetition, can be formed using TRIANGLE, where words should start with 'T' & end with 'E' ?

I think you should check options. If both the answers are there, then you should pick one in which number of all the possible words are found

1) For ROCKET, if all letters are used, then 6!, else
6 + 6^2 + 6^3 + .. + 6^6 (if repetition is allowed)
Else, 6! + C(6, 5)*5! + C(6, 4)*4! + C(6, 3)*3! + C(6, 2)*2! + 6

2) here TE are fixed, so 6!, if all letters are used, else
Same as in previous case, except that in both the cases their will be addition of 1 when their is no letter between T and E

Hi Puys,

Can someone please explain the method for solving below problems!

1) No. of ways of distributing 'n' similar objects into 'r' similar groups.

2) No. of ways of distributing 'n' distinct objects into 'r' similar groups.

Thanks in adv.
Anupam


I think there is no general formula for that, if you have some specific question in mind, then you can ask that.
409

12 villages in a district are divided into 3 zones wid 4 villages per zone.The telephone dept. tends to connect the villages with tellephone lines ssuch that every two villages in the same zone are connected wid 3 direct lines and every 2 villages belonging to different zones are connected wid 2 direct lines.How many direct lines are required?????

a.210
b.96
c.54
d.150plzz answer wid explanation