Coudn't get a simple combination exercise?
$begingroup$
Find how many 5-player teams could be made out of group 7 people:
- if the captain is already selected (from the same group of 7 people)
So, I know that I have to use: $_{n}C_{k} = frac{n!}{k!(n-k)!}$, to find all the combinations of $n$ items, selected $k$ at a time.
I can't seem to figure out the implication of the captain (pre)selection, i.e. how are $n$ and $k$ affected by the above constraint?
Every useful advice will be appreciated!
combinatorics combinations
asked Jan 15 at 13:27
ZieziZiezi
333520
$endgroup$
add a comment |
$begingroup$
Find how many 5-player teams could be made out of group 7 people:
- if the captain is already selected (from the same group of 7 people)
So, I know that I have to use: $_{n}C_{k} = frac{n!}{k!(n-k)!}$, to find all the combinations of $n$ items, selected $k$ at a time.
I can't seem to figure out the implication of the captain (pre)selection, i.e. how are $n$ and $k$ affected by the above constraint?
Every useful advice will be appreciated!
combinatorics combinations
asked Jan 15 at 13:27
ZieziZiezi
333520
$endgroup$
2
$begingroup$
Hint: If the captain has already been selected, then the remaining 4 members must come from a group of 6 people (everyone except the captain).
$endgroup$
– awkward
Jan 15 at 13:33
$begingroup$
Thanks for the hint! How many combinations do I need to calculate? One for the captain, one for the rest of the team?
$endgroup$
– Ziezi
Jan 15 at 13:42
3
$begingroup$
The way I interpret the problem is that one of the group is named Fred, and Fred will be the captain. So there is nothing to select, when it comes to the captain.
$endgroup$
– awkward
Jan 15 at 14:02
add a comment |
$begingroup$
Find how many 5-player teams could be made out of group 7 people:
- if the captain is already selected (from the same group of 7 people)
So, I know that I have to use: $_{n}C_{k} = frac{n!}{k!(n-k)!}$, to find all the combinations of $n$ items, selected $k$ at a time.
I can't seem to figure out the implication of the captain (pre)selection, i.e. how are $n$ and $k$ affected by the above constraint?
Every useful advice will be appreciated!
combinatorics combinations
asked Jan 15 at 13:27
ZieziZiezi
333520
$endgroup$
Find how many 5-player teams could be made out of group 7 people:
- if the captain is already selected (from the same group of 7 people)
So, I know that I have to use: $_{n}C_{k} = frac{n!}{k!(n-k)!}$, to find all the combinations of $n$ items, selected $k$ at a time.
I can't seem to figure out the implication of the captain (pre)selection, i.e. how are $n$ and $k$ affected by the above constraint?
Every useful advice will be appreciated!
combinatorics combinations
combinatorics combinations
asked Jan 15 at 13:27
ZieziZiezi
333520
asked Jan 15 at 13:27
ZieziZiezi
333520
asked Jan 15 at 13:27
ZieziZiezi
333520
asked Jan 15 at 13:27
ZieziZiezi
333520
asked Jan 15 at 13:27
ZieziZiezi
333520
333520
2
$begingroup$
Hint: If the captain has already been selected, then the remaining 4 members must come from a group of 6 people (everyone except the captain).
$endgroup$
– awkward
Jan 15 at 13:33
$begingroup$
Thanks for the hint! How many combinations do I need to calculate? One for the captain, one for the rest of the team?
$endgroup$
– Ziezi
Jan 15 at 13:42
3
$begingroup$
The way I interpret the problem is that one of the group is named Fred, and Fred will be the captain. So there is nothing to select, when it comes to the captain.
$endgroup$
– awkward
Jan 15 at 14:02
add a comment |
2
$begingroup$
Hint: If the captain has already been selected, then the remaining 4 members must come from a group of 6 people (everyone except the captain).
$endgroup$
– awkward
Jan 15 at 13:33
$begingroup$
Thanks for the hint! How many combinations do I need to calculate? One for the captain, one for the rest of the team?
$endgroup$
– Ziezi
Jan 15 at 13:42
3
$begingroup$
The way I interpret the problem is that one of the group is named Fred, and Fred will be the captain. So there is nothing to select, when it comes to the captain.
$endgroup$
– awkward
Jan 15 at 14:02
2
2
$begingroup$
Hint: If the captain has already been selected, then the remaining 4 members must come from a group of 6 people (everyone except the captain).
$endgroup$
– awkward
Jan 15 at 13:33
$begingroup$
Hint: If the captain has already been selected, then the remaining 4 members must come from a group of 6 people (everyone except the captain).
$endgroup$
– awkward
Jan 15 at 13:33
$begingroup$
Thanks for the hint! How many combinations do I need to calculate? One for the captain, one for the rest of the team?
$endgroup$
– Ziezi
Jan 15 at 13:42
$begingroup$
Thanks for the hint! How many combinations do I need to calculate? One for the captain, one for the rest of the team?
$endgroup$
– Ziezi
Jan 15 at 13:42
3
3
$begingroup$
The way I interpret the problem is that one of the group is named Fred, and Fred will be the captain. So there is nothing to select, when it comes to the captain.
$endgroup$
– awkward
Jan 15 at 14:02
$begingroup$
The way I interpret the problem is that one of the group is named Fred, and Fred will be the captain. So there is nothing to select, when it comes to the captain.
$endgroup$
– awkward
Jan 15 at 14:02
add a comment |
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2
$begingroup$
Hint: If the captain has already been selected, then the remaining 4 members must come from a group of 6 people (everyone except the captain).
$endgroup$
– awkward
Jan 15 at 13:33
$begingroup$
Thanks for the hint! How many combinations do I need to calculate? One for the captain, one for the rest of the team?
$endgroup$
– Ziezi
Jan 15 at 13:42
3
$begingroup$
The way I interpret the problem is that one of the group is named Fred, and Fred will be the captain. So there is nothing to select, when it comes to the captain.
$endgroup$
– awkward
Jan 15 at 14:02