jnu 2010

[manisha sachdeva]

ques 36)in an examination there are three multiple choice questions and each question has 4 choices.
number of ways in which a student can fail to get all the answers correct?

ques 37) a function is selected at random from all the functions of the set A= (1,2,3,...N) in to self.
the probability that the function selected is one to one is?

[AS]

36.no of ways= 4*4*4-1=63

[Akshay Jain]

There is only 1 way in which a student can answer all the questions correctly
so no. Of ways in wich a student fail to get all the answers is the same as the no of ways in which he attempts atleat 1 ques  incorrectly
so this is equal to total no. Of ways - 1(way in which all answers are correct)
= 4^3-1

[Anjali]

@Akshay plz have a look at this
http://discussion-forum.2150183.n2.nabble.com/DOUBTS-td7589558.html

[Bankelal]

Hi Manisha,

Sample space= n^n

f: A->A can be one-to-one

when for f(1) we have 1..n .ie n choices

for f(2)  n-1 choices...

...

f(n). 1 choice 

No. of one-one mappings possible= n(n-1)...1

ie. ans is n!/(n^n) Rahul(p....u)

On Tue, May 13, 2014 at 11:28 PM, manisha sachdeva [via Discussion forum] <[hidden email]> wrote:

ques 36)in an examination there are three multiple choice questions and each question has 4 choices.
number of ways in which a student can fail to get all the answers correct?

ques 37) a function is selected at random from all the functions of the set A= (1,2,3,...N) in to self.
the probability that the function selected is one to one is?

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[The Villain]

37 n!/n^n

[manisha sachdeva]

Rahul can u explain me why have u taken the sample space as n^n

I didnt geti t RAHUL :D

On Tuesday, May 13, 2014, Aditya [via Discussion forum] <[hidden email]> wrote:

Hi Manisha,

Sample space= n^n

f: A->A can be one-to-one

when for f(1) we have 1..n .ie n choices

for f(2)  n-1 choices...

...

f(n). 1 choice 

No. of one-one mappings possible= n(n-1)...1

ie. ans is n!/(n^n) Rahul(p....u)

On Tue, May 13, 2014 at 11:28 PM, manisha sachdeva [via Discussion forum] <[hidden email]> wrote:

ques 36)in an examination there are three multiple choice questions and each question has 4 choices.
number of ways in which a student can fail to get all the answers correct?

ques 37) a function is selected at random from all the functions of the set A= (1,2,3,...N) in to self.
the probability that the function selected is one to one is?

---

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[The Villain]

@manisha
Total no of functions fr the set to itself is n^n..
n favourable cases is n!

[Bankelal]

if we take f: A -> A

say 1 belongs to A, function f can be such that f(1) can be 1 or 2 or ...n. ie total n.

and for every x belongs to A, n possibilities exist...

thus n^n

On Wed, May 14, 2014 at 1:44 AM, manisha sachdeva [via Discussion forum] <[hidden email]> wrote:

Rahul can u explain me why have u taken the sample space as n^n

I didnt geti t RAHUL :D

On Tuesday, May 13, 2014, Aditya [via Discussion forum] <[hidden email]> wrote:

Hi Manisha,

Sample space= n^n

f: A->A can be one-to-one

when for f(1) we have 1..n .ie n choices

for f(2)  n-1 choices...

...

f(n). 1 choice 

No. of one-one mappings possible= n(n-1)...1

ie. ans is n!/(n^n) Rahul(p....u)

On Tue, May 13, 2014 at 11:28 PM, manisha sachdeva [via Discussion forum] <[hidden email]> wrote:

ques 36)in an examination there are three multiple choice questions and each question has 4 choices.
number of ways in which a student can fail to get all the answers correct?

ques 37) a function is selected at random from all the functions of the set A= (1,2,3,...N) in to self.
the probability that the function selected is one to one is?

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