## 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 ?

1. 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}}

2. steve816

40C1 * 40C4 I think that is the answer... btw, why are you only posting counting questions?

3. mathmath333

why not 40C1 *40C4 *5!

4. mathmath333

@steve816

5. steve816

Where did you get the 5! ?

6. mathmath333

to permutate 5 students

7. steve816

Actually, I think you might be right! 40C1 *40C4 *5!

8. mathmath333

r u 100% sure

9. steve816

Not a 100%, I struggled a little bit during probability unit too, but it seems right.

when a captain is chosen, there will be 39 left so shouldnt it be 40C1*39C4

11. mathmath333

but the 5 choosen students should be arranged in themselves

12. 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 = $$\dbinom{40}{5}*\dbinom{5}{1}$$

13. ganeshie8

btw thats same as 40C1*39C4

wow there are totally different ways to think of it.

Since the arrangement inside the group is not relavant 5! is not required

16. mathmath333

but in question the word 'arranged' is given

17. ganeshie8

question is ambiguous you can't do anything if the question is ambiguous

18. ganeshie8

19. mathmath333

yes 40 *39C4 is given answer

20. 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}}

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

ok but still max people gave 40C1*39C4 at first glance

23. ganeshie8

40C1*39C4 is same as 40*39C4

24. mathmath333

i m getting suspeciuos of my different approach of understanding

25. mathmath333

yea i know its same

26. mathmath333

thnks

27. anonymous

These questions are pretty fun to think about and solve.