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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 ?

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{ A bouquet has to be formed from 18 different flowers so}\ \hspace{.33em}\\~\\ & \normalsize \text{ that it should contain not less than 3 flowers. How many}\ \hspace{.33em}\\~\\ & \normalsize \text{ ways are there of doing this in ?}\ \hspace{.33em}\\~\\ & a.)\ 524288 \hspace{.33em}\\~\\ & b.)\ 262144 \hspace{.33em}\\~\\ & c.)\ 261972 \hspace{.33em}\\~\\ & d.)\ \normalsize \text{none of these} \hspace{.33em}\\~\\ \end{align}}\)

  2. ParthKohli
    • one year ago
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    I hope this isn't a circular permutations question, but just a normal combinations wala question.

  3. mathmath333
    • one year ago
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    Is it \(\large \color{black}{\begin{align} & 2^{18}-(1+2^{1}+2^{2}+2^{3})\hspace{.33em}\\~\\ \end{align}}\)

  4. mathmath333
    • one year ago
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    is answer option c.)

  5. ganeshie8
    • one year ago
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    The problem is equivalent to forming subsets with cardinality > 2 from a set with cardinality 18

  6. ParthKohli
    • one year ago
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    \[2^{18} - \left(\binom{18}{0} + \binom{18}{1}+\binom{18}{2}\right)\]

  7. ParthKohli
    • one year ago
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    oh no he beat me to it

  8. ParthKohli
    • one year ago
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    one day I'll get my internet speed upgraded... one day...

  9. mathmath333
    • one year ago
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    hey but the answer given is option d.) none

  10. ganeshie8
    • one year ago
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    lol PK I heard ACT provides higher speeds; mine is airtel, though http://www.acttv.in/index.php/products/act-broadband

  11. ganeshie8
    • one year ago
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    @mathmath333 does it give any explanation ? we might get a different answer if we interpret it differently

  12. mathmath333
    • one year ago
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    wait

  13. ganeshie8
    • one year ago
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    Anyways, this is a trivial question. I feel not worth spending time... must be a typo or a mistake of author..

  14. mathmath333
    • one year ago
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    It doesn't has any explanation \(\large \color{black}{\begin{align} & 2^{18}-(\dbinom{18}{0}+\dbinom{18}{1}+\dbinom{18}{2}+\dbinom{18}{3})=261158\hspace{.33em}\\~\\ \end{align}}\)

  15. ganeshie8
    • one year ago
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    you can have 3 flowers, so you should not subtract that

  16. ParthKohli
    • one year ago
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    I know about ACT but I'm from Delhi. And I have Airtel too.

  17. mathmath333
    • one year ago
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    ok i assume it to be typo

  18. ParthKohli
    • one year ago
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    OH YOU'RE FROM BANGALORE. I'm so jealous, Ganeshie.

  19. imqwerty
    • one year ago
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    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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