IIT JEE , AIEEE Forum - Mathematics , Algebra - P and C

MUDIT

THE NUMBER OF ALL POSSIBLE

SELECTIONS OF ONE OR MORE

QUESTIONS FROM 10 GIVEN

QUESTIONS,EACH QUESTION HAVING

ONE ALTERNATIVE IS

a) 3^10

b) 2^10 -1

c) 3^10 -1

d)2^10

THE ANSWER GIVEN IS (c) BUT I WOULD

PREFER A DETAILED SOLUTION.

rini

i think the answer should be (b)..

coz total selections=

(selecting 1 ques)+ (selecting 2 ques )+ - - - - - - - - +(selecting 10 ques)

= 10C1 +10C2 +10C3 + - - - - - - - - - - + 10C 10
= 2^10 -1.............(B)

MUDIT

BUT RINI IT ISIN'T THAT SIMPLE EACH QUESTION HAS ONE ALTERNATIVE WHICH HAS BEEN CLEARLY MENTIONED ABOVE.

nishantsingh89

can you please clear what does one alternative mean because as far as i guess it with each question you have three options :

a) you select it
b) you don't select it
c) well, the alternative which is present

if this is what alternative means here then the answer can be expained as below:
with each question you have 3 options
so total ways you can select question is 3^10
here now we subtract 1 case where we don't select any question
so the answer is
3^10 -1

rate me if correct

nadeemoidu

if "one alternative" means 2 choices, then here's the answer.

for each question u have 3 choices : option 1 , option 2, or to not select that question.

so for 10 questions u have 3^10 choices.

but u have to select one or more choices . so exclude the case where u do not choose any question.
so answer is 3^10 -1

priyesh

each question can be handled in 3 ways

either do the main question , or alternative , or leave it

so total selections possible are 3 * 3* 3......10times = 3^10

but question says one or more selections

so we remove the case in which the person leaves all the questions (i.e gives a blank paper)

hence no. of cases = 3^10 -1

MUDIT

ALL OF YOU HAVE DONE THE SAME THING AND I THINK THIS IS THE CORRECT SOLUTION BUT THE DOUBT I HAVE IS EVERY QUESTION HAS ONE ALTERNATIVE SO YOU CAN EITHER SELECT THE MAIN QUESTION OR THE ALTERNATIVE OR BOTH OR NONE OF THEM, SO EACH QUESTION CAN BE SELECTED IN 4 WAYS???

priyesh

no mudit how cannot select both the main & the alternative question

because you have to do any one of them that's why the name is ALTERNATIVE question

MUDIT

THANKS A LOT PRIYESH.

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