Permutations & Combinations - Questions & Discussions

MBA CAT 2022
369
Students score in each section is a, b, c, d, then

a + b + c + d = 90
=> C(93, 90) ways, but we have counted those cases also when a, b, c, d > 45

When a > 45, i.e., a = 46 + a'
=> a' + b + c + d = 44
=> C(47, 44) ways

Similarly for other variables

So, total number of ways = C(93, 90) - 4*C(47, 44) = 64096

I am not able understand this value C(93, 90) - 4*C(47, 44) ??

Could you any one pls eloborate and explain in detail ??

Thanks in advance !!
370
Students score in each section is a, b, c, d, then

a + b + c + d = 90
=> C(93, 90) ways, but we have counted those cases also when a, b, c, d > 45

When a > 45, i.e., a = 46 + a'
=> a' + b + c + d = 44
=> C(47, 44) ways

Similarly for other variables

So, total number of ways = C(93, 90) - 4*C(47, 44) = 64096

Chill bhai why are we taking only 90.A student with more than 90 marks(91,92,...180) also qualifies right???

P.S-pardon me if this is a silly question.Just a thought
371
Chill bhai why are we taking only 90.A student with more than 90 marks(91,92,...180) also qualifies right???

P.S-pardon me if this is a silly question.Just a thought


Yup my mistake. Thanks for the correction.

Lets say that a is the marks lost in one section, b in another, c is third and d in fourth.

So, (45 - a) + (45 - b) + (45 - c) + (45 - d) 90
a + b + c + d 90

So, C(94, 4) ways, but we have counted those cases also when a, b, c, d > 45

When a > 45, i.e., a = 46 + a'
=> a' + b + c + d 44
=> C(48, 4) ways

Similarly for other variables

So, total number of ways = C(94, 4) - 4*C(48, 4)
372

could any1 mail me the ebook of permutations and combinations......my email id is help me out frndzz...am posing a lot of problems in it

373

Someone please help me out here- "How many 4 digit numbers divisible by 5 can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 6?"

374
PAUL KINGSLEY Says
Someone please help me out here- "How many 4 digit numbers divisible by 5 can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 6?"

Doubt : do we have number 6 twice?? if yes should the numbers be identical???
or not necessarily??? or do u want both the cases???
375
Doubt : do we have number 6 twice?? if yes should the numbers be identical???
or not necessarily??? or do u want both the cases???


yes both 6's are identical. Would be glad if u would solve both the cases. Thanx.
376

In how many ways can 2 red ,3 black and 2 white pencils be arranged in a row such that
no two adjacent pencils are of the same colour?
Can any one solve this problem and give the detailed solun ?

377
In how many ways can 2 red ,3 black and 2 white pencils be arranged in a row such that
no two adjacent pencils are of the same colour?
Can any one solve this problem and give the detailed solun ?


is the answer 30?
378
In how many ways can 2 red ,3 black and 2 white pencils be arranged in a row such that
no two adjacent pencils are of the same colour?
Can any one solve this problem and give the detailed solun ?


wrong........
379
hey man why are posting again this here,
you didnt get the solution at quant thread?????


Hey Bro,
It was together posted on both the threads.. Anyways, sorry for the inconvenience caused
380

Hi all,
I am a new entrant to PG. I have gone through the posts. Here are some intresting PC questions. Please give your answers and working for common benefit. Thank You.

1)How many 4 digit numbers divisble by 5 can be formed from 0,1,2,3,4,5,6 and 6
-220,
-249,
-432,
-216,
-288

2)There are 6 pups and 4 cats.In how many ways can they be seated in a row such that no cats sit together

3)In how many ways can mn things br distributed equally among n groups

Please reply.
Thanks,
Sprih

381
PAUL KINGSLEY Says
yes both 6's are identical. Would be glad if u would solve both the cases. Thanx.


195??? will explain if its ryt.......... nahi to i ll scratch my head..........
option not der ... den 220......(edited)
382
Hi all,
I am a new entrant to PG. I have gone through the posts. Here are some intresting PC questions. Please give your answers and working for common benefit. Thank You.

1)How many 4 digit numbers divisble by 5 can be formed from 0,1,2,3,4,5,6 and 6
-220,
-249,
-432,
-216,
-288

2)There are 6 pups and 4 cats.In how many ways can they be seated in a row such that no cats sit together

3)In how many ways can mn things br distributed equally among n groups

Please reply.
Thanks,
Sprih


220
6!
mn+1

pls correct me if wrong
: to PG
384
DOUBT

In how many ways can a black square and a white square be chosen from a chessboard that they are either from the same row or same column.

(1) 512
(2) 256


My approach is 64 ways to select the first square and 8C1 to select the second.= 64x8= 512 ways

But apparently the order matters here as the solutions says

we can chose a black square in 32 ways and then a white square in 8 ways= 256 ways
385
DOUBT

In how many ways can a black square and a white square be chosen from a chessboard that they are either from the same row or same column.

(1) 512
(2) 256


My approach is 64 ways to select the first square and 8C1 to select the second.= 64x8= 512 ways

But apparently the order matters here as the solutions says

we can chose a black square in 32 ways and then a white square in 8 ways= 256 ways


if question reads black first and white second , obviously answer is 256

if nothing is mentioned , we can count 256 ways for black and 256 ways for white which adds up to 512
386

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?

387

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?

388

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?

389

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?