IIT JEE , AIEEE Forum - Mathematics , Algebra

prateek2292

if there are m men and n monkeys.

find the no. ways that each monkey has it's master?

abhijeet_0201

m^n
since each monkey can choose his master in m ways

m *m*m*m..........ntimes

=m^n

rooney

No.

I think in the ques, each man can have only 1 monkey as pet.

So answer is m(m-1)(m-2).....(m-n+1)

VIV

why cant we go like this->
1st man has n choices,
2nd man has n-1 choices and so on
ie.
(n)(n-1)(n-2).......(n-m+1)

please explain.

priyesh

@VIV

u can't go,in this direction because m>n for the situtation to be true

so if m>n
then by working ur way
after some time the man wont be left with a choice as all monkeys will be sold

rockey

it is m(m-1)............ (m-n+1)
since 1st monkey can choose its master in m ways , 2n d in (m-1) and so on

prateek2292

the ans is n^m.
u were close to it abhijeet.
Each master can chose n monkeys.
Therefore,
n*n*n.......m times=n^m.
however abhijeet how a monkey can choose his master.

abhijeet_0201

oh i am so sorry ..........silly of me!!!!

abhijeet_0201

hey wait a minute............i am correct!!!!!!!!

i dont mean a monkey will choose his master but a monkey can have his master in m ways(since there are m masters)
hence my ans

plz check ur ans!!

in the ques each monkey has to have a master not every master to have a monkey

so we have to see frm the monkey's perspective

anyways the reverse cant bring the correct ans since when one master has chosen a monkey then n-1 monkeys are left for others

hence the ans n^m can never come!!!!

dhabachatterjee

each monkey can have its master in m ways .so n(to the power)m

abhijeet_0201

@dhabachatterjee

each monkey can have its master in m ways
so it will be m^n(m**m*m*m*m...n times)
sont u think so?????????

rockey

abhijeet i think u are correct

bhartibhanushali

each monkey chooses his master
it means that 2 or more monkey can have same masters

hence all the monkey can choose their master in m ways
hence total ways is m*m*m*m*m*m*m*m*m*m*m*m*m.......n times

hence answer is m^n
matches with abhijeet answers!!

prateek2292

it's not so abhijeet.
in this cond. is m>n.
it is necessary that each monkey should have atleast one master.
Considering what u r saying,
if one monkey selects his master in m ways.
then at that very cond. how can other monkeys have there respective masters.
then the cond. of having atleast one master is violated.
But when a master choose his monkey then he can choose n monkeys which in turn will also satisfy the cond.
therefore the ans is
n*n*n*...........m times=n^m.

prateek2292

please rate me if u r satisfied....

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