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Question Number 201729 by hardmath last updated on 11/Dec/23
The teacher can choose in 560 ways, provided that there are three students in each team.  Knowing that five students do not want to participate, find the number of people willing to participate
The teacher can choose in 560 ways, provided that there are three students in each team. Knowing that five students do not want to participate, find the number of people willing to participate
Commented by mr W last updated on 11/Dec/23
you didn′t state clearly enough,  what the teacher does? what does  the teacher choose in 560 ways?
$${you}\:{didn}'{t}\:{state}\:{clearly}\:{enough}, \\ $$$${what}\:{the}\:{teacher}\:{does}?\:{what}\:{does} \\ $$$${the}\:{teacher}\:{choose}\:{in}\:\mathrm{560}\:{ways}? \\ $$
Commented by mr W last updated on 11/Dec/23
when you just want to find how many  people are willing to participate,  then it doesn′t matter how many  people don′t want to participate.
$${when}\:{you}\:{just}\:{want}\:{to}\:{find}\:{how}\:{many} \\ $$$${people}\:{are}\:{willing}\:{to}\:{participate}, \\ $$$${then}\:{it}\:{doesn}'{t}\:{matter}\:{how}\:{many} \\ $$$${people}\:{don}'{t}\:{want}\:{to}\:{participate}. \\ $$
Commented by hardmath last updated on 11/Dec/23
yes dear professor
$$\mathrm{yes}\:\mathrm{dear}\:\mathrm{professor} \\ $$
Commented by hardmath last updated on 11/Dec/23
dear professor, Is there a solution?
$$\mathrm{dear}\:\mathrm{professor},\:\mathrm{Is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{solution}? \\ $$
Commented by mr W last updated on 11/Dec/23
the first sentence is cut off. if you  even don′t know what it is, how can  i know?
$${the}\:{first}\:{sentence}\:{is}\:{cut}\:{off}.\:{if}\:{you} \\ $$$${even}\:{don}'{t}\:{know}\:{what}\:{it}\:{is},\:{how}\:{can} \\ $$$${i}\:{know}? \\ $$
Commented by mr W last updated on 11/Dec/23
when it′s not clear what your question  is, how is a solution possible?
$${when}\:{it}'{s}\:{not}\:{clear}\:{what}\:{your}\:{question} \\ $$$${is},\:{how}\:{is}\:{a}\:{solution}\:{possible}? \\ $$
Commented by mr W last updated on 11/Dec/23
i have asked you:  what does the teacher choose in   560 ways?
$${i}\:{have}\:{asked}\:{you}: \\ $$$${what}\:{does}\:{the}\:{teacher}\:{choose}\:{in}\: \\ $$$$\mathrm{560}\:{ways}? \\ $$
Commented by mr W last updated on 11/Dec/23
or when you read your question, do  you understand your question?
$${or}\:{when}\:{you}\:{read}\:{your}\:{question},\:{do} \\ $$$${you}\:{understand}\:{your}\:{question}? \\ $$
Commented by hardmath last updated on 11/Dec/23
  Dear professor for example, what might be the right condition
$$ \\ $$Dear professor for example, what might be the right condition
Commented by hardmath last updated on 11/Dec/23
  I don't know, dear professor, it was given on the condition that I asked for help
$$ \\ $$I don't know, dear professor, it was given on the condition that I asked for help
Answered by esmaeil last updated on 11/Dec/23
 (((n−5)),(3) )=56o→  (((n−5)!)/(3!(n−8)!))=560→  (n−5)(n−6)(n−7)=3360  n=21
$$\begin{pmatrix}{{n}−\mathrm{5}}\\{\mathrm{3}}\end{pmatrix}=\mathrm{56}{o}\rightarrow \\ $$$$\frac{\left({n}−\mathrm{5}\right)!}{\mathrm{3}!\left({n}−\mathrm{8}\right)!}=\mathrm{560}\rightarrow \\ $$$$\left({n}−\mathrm{5}\right)\left({n}−\mathrm{6}\right)\left({n}−\mathrm{7}\right)=\mathrm{3360} \\ $$$${n}=\mathrm{21} \\ $$
Commented by mr W last updated on 11/Dec/23
what is the question?   21 willing people? but 5 among them  do not want to participate? then  they are not willing people.
$${what}\:{is}\:{the}\:{question}?\: \\ $$$$\mathrm{21}\:{willing}\:{people}?\:{but}\:\mathrm{5}\:{among}\:{them} \\ $$$${do}\:{not}\:{want}\:{to}\:{participate}?\:{then} \\ $$$${they}\:{are}\:{not}\:{willing}\:{people}. \\ $$

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