1. ## combination questions

i have a little bit understanding problam....
1.basketball team have 10 players, how many posibilities the coach have to peek 5 players
so i did 10C5, and this is the correct answer in the book
but why 10*9*8*7*6 is not a good answer???
the coach have at the first peek 10 posibilities then 9 then 8.... so why this is wrong???

2. for a mission there is need to peek 2 officers of 5 and 3 soldiers of 8
how many posebilities exist?
so i did 5C2 * 8C3, but the answers in the book show that its a wrong answer. the good one is 5*4*8*7*6. im understand the process. that the first officer is 5 posibilities then 4 and soldiers is 8 posibilities the 7 then 6
but why the answer is in this whay and not 5C2 * 8C3 ??????

2. Originally Posted by tukilala
1.basketball team have 10 players, how many posibilities the coach have to pick 5 players. Why 10*9*8*7*6 is not a good answer???
Because the order in which the coach chooses the players does not matter.
This is a content driven question. As such, we use combinations.
What you have suggested is a permutation where order is the driving consideration.

Originally Posted by tukilala
2. for a mission there is need to pick 2 officers of 5 and 3 soldiers of 8 how many possibilities exist?
5C2 * 8C3 is correct.
Again, order makes no difference we only care about content (the makeup of the team).

3. and if the question is like that:
for a mission there is need to pick first offices, lieutenant that he is an officer too and 3 soldiers that they are not officers and there professionalization are: infantryman ,signal operator and machine gunner
the team is picken from 5 officers and 8 soldiers
how many posibilities can i choose the team?
is the answer is 5C2 * 8C3
or now its (8!\5!) * (5!\3!) and if yes, so why?
where is the order???? why i cant pick 2 offisers of five?? and 3 soldiers of 8? why i need the order?

4. Originally Posted by tukilala
and if the question is like that:
for a mission there is need to pick first offices, lieutenant that he is an officer too and 3 soldiers that they are not officers and there professionalization are: infantryman ,signal operator and machine gunner the team is picken from 5 officers and 8 soldiers
how many posibilities can i choose the team? is the answer is 5C2 * 8C3
I must say that I have a very hard time reading the above.
But yes the answer is still 5C2 * 8C3.
Change the question to this, “Pick an officer to be in charge, pick an officer to be her assistant. Then from the other group pick someone to be an infantryman, someone to be a signal operator and someone to be a machine gunner.
Now we have TWO permutations $\left(\frac{5!}{3!}\right) \left(\frac{8!}{5!}\right)$.