Comb.

[Elita]

There are 6 Questions on a question paper. In how many ways can a student solve one or more questions?

a)6 b)12 c)63 d)64 e)65

[shanmukh]

is it 63

[smtripathi]

yep it's 63.

2(6) - 1
=63.

[Elita]

Thanks guys for your reply.

Answer is (C). But I don't understand the way you reach that.

Why do you subtract 1 from 2^6?

And the Q asks in how many ways can you solve ONE OR MORE QUESTIONS?
What does it mean - the ways to solve all 6 Questions, or just one + some more, but how many??

I am totally confused with this one... PLease, help

[scorer]

2^6 - 1 is the shortest way, though understanding the mechanics is important.

Total Combinations = nCr.
Where n = 6.
r = 1..6. (no zero because, atleast one question has to be solved)
so 6C1+6C2+...+6C6 = 63.

[nikki_parekh]

6c1+6c2+6c3+6c4+6c5+6c6=63

[Elita]

2^6 - 1 is the shortest way, though understanding the mechanics is important.

Total Combinations = nCr.
Where n = 6.
r = 1..6. (no zero because, atleast one question has to be solved)
so 6C1+6C2+...+6C6 = 63.

Thank you Scorer!!!
It is much, much clear now

[indoatlantic]

how did u get 2^6?? Please help !! Thnx

[udaygrover]

Look at it like this

there are 2 options with each question
1. u solve it
2. u dont solve it

so possible ways are 2 for each question

now if u have 2 questions

possible ways =2*2

extend the logic to 6 q's
possible ways = 2^6

hope it clears some doubts

n we reduce the 1 in the answer...
well im sure every1 knows that by now

uday

[300IS]

2 dumb Qs here.

1) nCr. how does this work? 6C1 = ? 6C2 = ?

2) why do we minus 1? uday, sorry, i just want to confirm it. Is it because we have to answer at least 1 correct answer? so getting all 6 wrongs is not an option.