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

Question

mathmath333 · Answer

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

steve816 · Answer

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

mathmath333 · Answer

why not 40C1 *40C4 *5!

mathmath333 · Answer

@steve816

steve816 · Answer

Where did you get the 5! ?

mathmath333 · Answer

to permutate 5 students

steve816 · Answer

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

mathmath333 · Answer

r u 100% sure

steve816 · Answer

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

badhi · Answer

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

mathmath333 · Answer

but the 5 choosen students should  be arranged in themselves

ganeshie8 · Answer

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 · Answer

btw thats same as 40C1*39C4

badhi · Answer

wow there are totally different ways to think of it.

badhi · Answer

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

mathmath333 · Answer

but in question the word 'arranged' is given

ganeshie8 · Answer

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

ganeshie8 · Answer

do you have answer ?

mathmath333 · Answer

yes 40 *39C4 is given answer

ganeshie8 · Answer

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 · Answer

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 · Answer

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

ganeshie8 · Answer

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

mathmath333 · Answer

i m getting suspeciuos of my different approach of understanding

mathmath333 · Answer

yea i know its same

mathmath333 · Answer

thnks

jhannybean · Answer

These questions are pretty fun to think about and solve.