mathmath333
  • mathmath333
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 ?
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{ A bouquet has to be formed from 18 different flowers so}\ \hspace{.33em}\\~\\ & \normalsize \text{ that it should contain not less than 3 flowers. How many}\ \hspace{.33em}\\~\\ & \normalsize \text{ ways are there of doing this in ?}\ \hspace{.33em}\\~\\ & a.)\ 524288 \hspace{.33em}\\~\\ & b.)\ 262144 \hspace{.33em}\\~\\ & c.)\ 261972 \hspace{.33em}\\~\\ & d.)\ \normalsize \text{none of these} \hspace{.33em}\\~\\ \end{align}}\)
ParthKohli
  • ParthKohli
I hope this isn't a circular permutations question, but just a normal combinations wala question.
mathmath333
  • mathmath333
Is it \(\large \color{black}{\begin{align} & 2^{18}-(1+2^{1}+2^{2}+2^{3})\hspace{.33em}\\~\\ \end{align}}\)

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More answers

ganeshie8
  • ganeshie8
http://www.wolframalpha.com/input/?i=2%5E18+-+%2818+choose+0%29+-++%2818+choose+1%29+-+%2818+choose+2%29+
mathmath333
  • mathmath333
is answer option c.)
ganeshie8
  • ganeshie8
The problem is equivalent to forming subsets with cardinality > 2 from a set with cardinality 18
ParthKohli
  • ParthKohli
\[2^{18} - \left(\binom{18}{0} + \binom{18}{1}+\binom{18}{2}\right)\]
ParthKohli
  • ParthKohli
oh no he beat me to it
ParthKohli
  • ParthKohli
one day I'll get my internet speed upgraded... one day...
mathmath333
  • mathmath333
hey but the answer given is option d.) none
ganeshie8
  • ganeshie8
lol PK I heard ACT provides higher speeds; mine is airtel, though http://www.acttv.in/index.php/products/act-broadband
ganeshie8
  • ganeshie8
@mathmath333 does it give any explanation ? we might get a different answer if we interpret it differently
mathmath333
  • mathmath333
wait
ganeshie8
  • ganeshie8
Anyways, this is a trivial question. I feel not worth spending time... must be a typo or a mistake of author..
mathmath333
  • mathmath333
It doesn't has any explanation \(\large \color{black}{\begin{align} & 2^{18}-(\dbinom{18}{0}+\dbinom{18}{1}+\dbinom{18}{2}+\dbinom{18}{3})=261158\hspace{.33em}\\~\\ \end{align}}\)
ganeshie8
  • ganeshie8
you can have 3 flowers, so you should not subtract that
ParthKohli
  • ParthKohli
I know about ACT but I'm from Delhi. And I have Airtel too.
mathmath333
  • mathmath333
ok i assume it to be typo
ParthKohli
  • ParthKohli
OH YOU'RE FROM BANGALORE. I'm so jealous, Ganeshie.
imqwerty
  • 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

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