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mathmath333

  • one year ago

There are 40 students .In how many ways can they be arranged to form a team with 1 captain and 4 vice-captains ?

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{There are 40 students .In how many ways can they be arranged to}\hspace{.33em}\\~\\ & \normalsize \text{ form a team with 1 captain and 4 vice-captains ? }\hspace{.33em}\\~\\ \end{align}}\)

  2. steve816
    • one year ago
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    40C1 * 40C4 I think that is the answer... btw, why are you only posting counting questions?

  3. mathmath333
    • one year ago
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    why not 40C1 *40C4 *5!

  4. mathmath333
    • one year ago
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    @steve816

  5. steve816
    • one year ago
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    Where did you get the 5! ?

  6. mathmath333
    • one year ago
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    to permutate 5 students

  7. steve816
    • one year ago
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    Actually, I think you might be right! 40C1 *40C4 *5!

  8. mathmath333
    • one year ago
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    r u 100% sure

  9. steve816
    • one year ago
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    Not a 100%, I struggled a little bit during probability unit too, but it seems right.

  10. BAdhi
    • one year ago
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    when a captain is chosen, there will be 39 left so shouldnt it be 40C1*39C4

  11. mathmath333
    • one year ago
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    but the 5 choosen students should be arranged in themselves

  12. ganeshie8
    • one year ago
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    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 = \(\dbinom{40}{5}*\dbinom{5}{1}\)

  13. ganeshie8
    • one year ago
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    btw thats same as 40C1*39C4

  14. BAdhi
    • one year ago
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    wow there are totally different ways to think of it.

  15. BAdhi
    • one year ago
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    Since the arrangement inside the group is not relavant 5! is not required

  16. mathmath333
    • one year ago
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    but in question the word 'arranged' is given

  17. ganeshie8
    • one year ago
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    question is ambiguous you can't do anything if the question is ambiguous

  18. ganeshie8
    • one year ago
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    do you have answer ?

  19. mathmath333
    • one year ago
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    yes 40 *39C4 is given answer

  20. ganeshie8
    • one year ago
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    then read the question like this : \[ \large \color{black}{\begin{align} & \normalsize \text{There are 40 students. How many ways can a 5 member team }\hspace{.33em}\\~\\ & \normalsize \text{ with 1 captain and 4 normal players be formed ?}\hspace{.33em}\\~\\ \end{align}} \]

  21. BAdhi
    • one year ago
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    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

  22. mathmath333
    • one year ago
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    ok but still max people gave 40C1*39C4 at first glance

  23. ganeshie8
    • one year ago
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    40C1*39C4 is same as 40*39C4

  24. mathmath333
    • one year ago
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    i m getting suspeciuos of my different approach of understanding

  25. mathmath333
    • one year ago
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    yea i know its same

  26. mathmath333
    • one year ago
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    thnks

  27. Jhannybean
    • one year ago
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    These questions are pretty fun to think about and solve.

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