Permutations & Combinations - Questions & Discussions

MBA CAT 2022
812
puyz help
In an examination the maximum marks for each of the three papers are 50 each. Max marks for the fourth paper are 100. Find the number of ways in which the candidate cans score 60 percent marks in aggregate
I have solved this as 153c3-52c3-3*102c3=48076...but OA is given as 110551..
What am I missing??

813
Find the number of integral solution of |x| + |y| + |z| =10
a)402
b)304
c)202
d)502
814
@admantium said:
Find the number of integral solution of |x| + |y| + |z| =10 a)402 b)304 c)202 d)502
is it 402 ?
815

answer is 202....?

816

@gs4890 said:
is it 402 ?
@swap747 said:
answer is 202....?
I do not know the answer :(.... plz explain how you got those answers... Thnx in advance
817

i considered cases...all three non -ve...12C2 ....one negative 11C2....two negative 10C2...and all three negative 9C2....adding all...202

818
@swap747 said:
i considered cases...all three non -ve...12C2 ....one negative 11C2....two negative 10C2...and all three negative 9C2....adding all...202
I think it shud be 402..... ur approach is spot on but one no. can be negative in 3 ways and similarly 3 pairs of nos can be negative. therefore, 12C2+3*11C2+3*10C2+9C2= 402
819

oh yeah u r right...:) thanx @sayanddude

820

How can we select three shoes which includes a pair of shoes from 10 paris of shoes ?

I solve it like 20 ways to choosing 1st shoe and 1 way of choosing another shoe ..18 ways to the third shoe..... 20x18 = 360

Others solve it like 10 ways of choosing the right pair..18 ways of choosing the other shoe....

10x18 = 180

As usuall others are right

Whats the logic puys...pls help

821

if N=3^a*3^b, a and b are any two integers whose range is from 1 to 6 what is the probability that N is a multiple of 729.
a. 5/18 b. 5/11 c. 13/11 d. 13/18 e. none

822
@nik25 said:
if N=3^a*3^b, a and b are any two integers whose range is from 1 to 6 what is the probability that N is a multiple of 729.
a. 5/18 b. 5/11 c. 13/11 d. 13/18 e. none
5/11
823
@maddy2807 i am getting 5/18...can u please explain how is it 5/11?
824
@swap747 said:
@maddy2807 i am getting 5/18...can u please explain how is it 5/11?
since a+b=6
this can be done in 5 ways.
and a+b=12
this in 11 ways.
how did u do it. I might b wrng.
825
@swap747 can you please explain the process ?
826
@swap747 for N to be a multiple of 729 i.e. 3^6, a+b should be >=6 but a+b=6 -- 5 ways
a+b=7 -- 6ways and so on total will be 45.

and total number of ways is 55 so 45/55=9/11. but i am not sure. can anyone tell me whether this is right or wrong ?
827
@nik25 dude, one thing i am not getting is, 55? the total number of set of values of a,b are 36. for it to be a multiple it has to >=6 and

earlier, i did a blunder, was trying to find divisors instead of multiples ...so was getting 5/18..:(
i am still not sure...
828
@nik 25 posted the question, hoping someone wud come up with a proper explanation to that
829
@swap747 a+b can take values from 2 to 12, but N will be a multiple only when a+b is 6,7,8,9,10,11,12. a+b=2 --1 way, a+b=3 --2 ways in this way total will be 55 (1+2+3+...11)
830

@nik25 dude....its not 55...u r correct till a+b =7 but for a+b= 8 its not 7, rather its 5 and it decreases from then i.e for a+b= 12...its a=6 and b=6 so 1way. in any case maximum number of sets possible are 36. so even if u get 55, some have to be redundant.
831
@swap747 yup u are correct..then i guess the answer is 13/18. (26/36)