sanju09 wrote:Mr. X and Mrs. Y are among the 8 persons out of which 6 are to be chosen as chief guests to a party. If Mr. X is chosen, then Mrs. Y becomes a MUST to be chosen. In how many ways can the selection be made?
(A) 6
(B) 15
(C) 16
(D) 21
(E) 22

Case 1:-Mr. X is chosen
Case 2:-Mrs.Y chosen but Mr X isn't
Case 3:-Both are not chosen


The imp. point to be kept in mind is that people can make a mistake of leaving case 2.

sanju09 wrote:Mr. X and Mrs. Y are among the 8 persons out of which 6 are to be chosen as chief guests to a party. If Mr. X is chosen, then Mrs. Y becomes a MUST to be chosen. In how many ways can the selection be made?
(A) 6
(B) 15
(C) 16
(D) 21
(E) 22

If Mr X and Mrs Y are out - there is only 1 way .. select all the other 6
If Mr X and Mrs Y are in - There 6C4 ways to select 4 out of 6; 6*5/2 = 15 ways

Total no of ways = 1+15 =16

ajith wrote:
If Mr X and Mrs Y are out - there is only 1 way .. select all the other 6
If Mr X and Mrs Y are in - There 6C4 ways to select 4 out of 6; 6*5/2 = 15 ways

Total no of ways = 1+15 =16

I did not consider Mrs Y is in and Mr X is out

We have select 5 out of 6 = 6 Ways

The answer becomes 16+6 = 22

Nice trap, Sanju .. I loved the question

ajith wrote:

ajith wrote:
If Mr X and Mrs Y are out - there is only 1 way .. select all the other 6
If Mr X and Mrs Y are in - There 6C4 ways to select 4 out of 6; 6*5/2 = 15 ways

Total no of ways = 1+15 =16

I did not consider Mrs Y is in and Mr X is out

We have select 5 out of 6 = 6 Ways

The answer becomes 16+6 = 22

Nice trap, Sanju .. I loved the question

Hey ajith ,
You fell into the trap and left out the case 2 that I had mentioned above
Mainly the imp. part to confuse was the use ofmust in the sentence.It makes our mind to register that when Mrs.Y is there then also Mr.X would be selected.
I guess most of the people will fall in this trap.
Nice question sanju.
Though I would like to ask you "sanju" if you have yourself set this trap in the question(I think the question was designed by you only-Nice one though)

harsh.champ wrote:

Though I would like to ask you "sanju" if you have yourself set this trap in the question(I think the question was designed by you only-Nice one though)

Thanks harsh and ajith in particular for liking and falling and then again liking the so called TRAP, when I solve a question that's made up by m e, I just love toying with the numbers that could have become an answer in the absence of an inner vision, and the same are there in the choices too. This is just one like that. NJOY

sanju09 wrote:harsh.champ wrote:

Though I would like to ask you "sanju" if you have yourself set this trap in the question(I think the question was designed by you only-Nice one though)

Thanks harsh and ajith in particular for liking and falling and then again liking the so called TRAP, when I solve a question that's made up by m e, I just love toying with the numbers that could have become an answer in the absence of an inner vision, and the same are there in the choices too. This is just one like that. NJOY

Hey,I got you.I had been seeing that the questions that you have posted always has an inner side to it.Also,you are very good in distorting the sentences.Also,in ur profiel ,it is written that you are a faculty in quantitaive,so I speculated that maybe this one is one of ur self-made questions.
Anyways,thanks for posting such questions.Solving such problems helps us to keep our vigil ante high and helps us to get accustomed with probable traps in the questions.

Also earlier I had made a suggestion to the BTG team for making a separate forum for trick questions.
In the sub-forums then,we can have MATH and VERBAl separately.
I guess that would help.

harsh.champ wrote:

In the sub-forums then,we can have MATH and VERBAl separately.

VERBAl seems to be a bit weak owing to that broken lIMB.

Anyways...Nice Idea Sir G

sanju09 wrote:Mr. X and Mrs. Y are among the 8 persons out of which 6 are to be chosen as chief guests to a party. If Mr. X is chosen, then Mrs. Y becomes a MUST to be chosen. In how many ways can the selection be made?
(A) 6
(B) 15
(C) 16
(D) 21
(E) 22

3 CASES

1) NO X AND Y NO OF WAYS =1
2) Y BUT NO X NO OF WAYS=6
3)X AND Y BTH ARE IN NO OF WAYS=6C4=15

TOT=22
e