Question

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 ?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

http://www.wolframalpha.com/input/?i=2%5E18+-+%2818+choose+0%29+-++%2818+choose+1%29+-+%2818+choose+2%29+

Answer 5

is answer option c.)

Answer 6

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

Answer 7

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

Answer 8

oh no he beat me to it

Answer 9

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

Answer 10

hey but the answer given is option d.) none

Answer 11

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

Answer 12

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

Answer 13

wait

Answer 14

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

Answer 15

It doesn't has any explanation


\(\large \color{black}{\begin{align}
& 2^{18}-(\dbinom{18}{0}+\dbinom{18}{1}+\dbinom{18}{2}+\dbinom{18}{3})=261158\hspace{.33em}\\~\\
\end{align}}\)

Answer 16

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

Answer 17

I know about ACT but I'm from Delhi.

And I have Airtel too.

Answer 18

ok i assume it to be typo

Answer 19

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

Answer 20

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