mathmath333
  • mathmath333
There are 40 students .In how many ways can they be arranged to form a team with 1 captain and 4 vice-captains ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{There are 40 students .In how many ways can they be arranged to}\hspace{.33em}\\~\\ & \normalsize \text{ form a team with 1 captain and 4 vice-captains ? }\hspace{.33em}\\~\\ \end{align}}\)
steve816
  • steve816
40C1 * 40C4 I think that is the answer... btw, why are you only posting counting questions?
mathmath333
  • mathmath333
why not 40C1 *40C4 *5!

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More answers

mathmath333
  • mathmath333
@steve816
steve816
  • steve816
Where did you get the 5! ?
mathmath333
  • mathmath333
to permutate 5 students
steve816
  • steve816
Actually, I think you might be right! 40C1 *40C4 *5!
mathmath333
  • mathmath333
r u 100% sure
steve816
  • steve816
Not a 100%, I struggled a little bit during probability unit too, but it seems right.
BAdhi
  • BAdhi
when a captain is chosen, there will be 39 left so shouldnt it be 40C1*39C4
mathmath333
  • mathmath333
but the 5 choosen students should be arranged in themselves
ganeshie8
  • ganeshie8
Alternative : You can choose 5 ppl for the team in \(\dbinom{40}{5}\) ways for each of that 5 member team, a captain can be chosen in \(\dbinom{5}{1}\) ways so total possible teams = \(\dbinom{40}{5}*\dbinom{5}{1}\)
ganeshie8
  • ganeshie8
btw thats same as 40C1*39C4
BAdhi
  • BAdhi
wow there are totally different ways to think of it.
BAdhi
  • BAdhi
Since the arrangement inside the group is not relavant 5! is not required
mathmath333
  • mathmath333
but in question the word 'arranged' is given
ganeshie8
  • ganeshie8
question is ambiguous you can't do anything if the question is ambiguous
ganeshie8
  • ganeshie8
do you have answer ?
mathmath333
  • mathmath333
yes 40 *39C4 is given answer
ganeshie8
  • ganeshie8
then read the question like this : \[ \large \color{black}{\begin{align} & \normalsize \text{There are 40 students. How many ways can a 5 member team }\hspace{.33em}\\~\\ & \normalsize \text{ with 1 captain and 4 normal players be formed ?}\hspace{.33em}\\~\\ \end{align}} \]
BAdhi
  • BAdhi
but in common sense, if we take a team, the team will not change if the team members are arranged in a different order. The team will be the same
mathmath333
  • mathmath333
ok but still max people gave 40C1*39C4 at first glance
ganeshie8
  • ganeshie8
40C1*39C4 is same as 40*39C4
mathmath333
  • mathmath333
i m getting suspeciuos of my different approach of understanding
mathmath333
  • mathmath333
yea i know its same
mathmath333
  • mathmath333
thnks
Jhannybean
  • Jhannybean
These questions are pretty fun to think about and solve.

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