mathmath333 one year ago A bouquet has to be formed from 18 different flowers so that it should contain not less than 3 flowers. How many ways are there of doing this in ?

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{ A bouquet has to be formed from 18 different flowers so}\ \hspace{.33em}\\~\\ & \normalsize \text{ that it should contain not less than 3 flowers. How many}\ \hspace{.33em}\\~\\ & \normalsize \text{ ways are there of doing this in ?}\ \hspace{.33em}\\~\\ & a.)\ 524288 \hspace{.33em}\\~\\ & b.)\ 262144 \hspace{.33em}\\~\\ & c.)\ 261972 \hspace{.33em}\\~\\ & d.)\ \normalsize \text{none of these} \hspace{.33em}\\~\\ \end{align}}

2. ParthKohli

I hope this isn't a circular permutations question, but just a normal combinations wala question.

3. mathmath333

Is it \large \color{black}{\begin{align} & 2^{18}-(1+2^{1}+2^{2}+2^{3})\hspace{.33em}\\~\\ \end{align}}

4. ganeshie8
5. mathmath333

6. ganeshie8

The problem is equivalent to forming subsets with cardinality > 2 from a set with cardinality 18

7. ParthKohli

$2^{18} - \left(\binom{18}{0} + \binom{18}{1}+\binom{18}{2}\right)$

8. ParthKohli

oh no he beat me to it

9. ParthKohli

one day I'll get my internet speed upgraded... one day...

10. mathmath333

hey but the answer given is option d.) none

11. ganeshie8

lol PK I heard ACT provides higher speeds; mine is airtel, though http://www.acttv.in/index.php/products/act-broadband

12. ganeshie8

@mathmath333 does it give any explanation ? we might get a different answer if we interpret it differently

13. mathmath333

wait

14. ganeshie8

Anyways, this is a trivial question. I feel not worth spending time... must be a typo or a mistake of author..

15. mathmath333

It doesn't has any explanation \large \color{black}{\begin{align} & 2^{18}-(\dbinom{18}{0}+\dbinom{18}{1}+\dbinom{18}{2}+\dbinom{18}{3})=261158\hspace{.33em}\\~\\ \end{align}}

16. ganeshie8

you can have 3 flowers, so you should not subtract that

17. ParthKohli

I know about ACT but I'm from Delhi. And I have Airtel too.

18. mathmath333

ok i assume it to be typo

19. ParthKohli

OH YOU'RE FROM BANGALORE. I'm so jealous, Ganeshie.

20. imqwerty

yea c is correct ok the number of ways wuld be 18C0+18C1+18C2 + 18C3+18C4+18C5........18C18-18C0 - 18C1 -18C2 $2^\left( 18 \right)-1-18-153$ =261972