In how many ways can 10 postcards be posted into 6 letterboxes ?
a) 10^6
b) 6^10
c) 10C6(10)
d) 10P6
e) 10P6(6)
OA b
Postcards and Postboxes
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Hey Gughan,
This is a weird sort of combinatorics question, which I would solve with the slots method:
1. Find # of slots (decisions to be made)
2. Fill in possibilities at each decision point
3. Figure out if Order matters or not (or a hybrid)
4. If order matters, multiply all slots together; if order doesn't matter, multiply all slots and divide by # of slots factorial wherever order doesn't matter.
In this case, we have to make 10 decisions, because every postcard has to be mailed. We need to decide which of the 6 mailboxes to put each mailbox in.
_ _ _ _ _ _ _ _ _ _
For each postcard, we have 6 choices. This pool never drops down (as it does in most combinatorics questions), because there's no limit to how many postcards we can put in each letterbox:
6 6 6 6 6 6 6 6 6 6
The answer is thus [spoiler]6^10[/spoiler].
-t
This is a weird sort of combinatorics question, which I would solve with the slots method:
1. Find # of slots (decisions to be made)
2. Fill in possibilities at each decision point
3. Figure out if Order matters or not (or a hybrid)
4. If order matters, multiply all slots together; if order doesn't matter, multiply all slots and divide by # of slots factorial wherever order doesn't matter.
In this case, we have to make 10 decisions, because every postcard has to be mailed. We need to decide which of the 6 mailboxes to put each mailbox in.
_ _ _ _ _ _ _ _ _ _
For each postcard, we have 6 choices. This pool never drops down (as it does in most combinatorics questions), because there's no limit to how many postcards we can put in each letterbox:
6 6 6 6 6 6 6 6 6 6
The answer is thus [spoiler]6^10[/spoiler].
-t
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Thanx Tom. I have a weird doubt now
Question : In how many ways can 6 letterboxes be posted with 10 postcards ?
Thanx in advance !
Cheers,
Gughan
Question : In how many ways can 6 letterboxes be posted with 10 postcards ?
Thanx in advance !
Cheers,
Gughan
Tommy Wallach wrote:Hey Gughan,
This is a weird sort of combinatorics question, which I would solve with the slots method:
1. Find # of slots (decisions to be made)
2. Fill in possibilities at each decision point
3. Figure out if Order matters or not (or a hybrid)
4. If order matters, multiply all slots together; if order doesn't matter, multiply all slots and divide by # of slots factorial wherever order doesn't matter.
In this case, we have to make 10 decisions, because every postcard has to be mailed. We need to decide which of the 6 mailboxes to put each mailbox in.
_ _ _ _ _ _ _ _ _ _
For each postcard, we have 6 choices. This pool never drops down (as it does in most combinatorics questions), because there's no limit to how many postcards we can put in each letterbox:
6 6 6 6 6 6 6 6 6 6
The answer is thus [spoiler]6^10[/spoiler].
-t
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Hey Gughan,
You just asked the same question!
What you may have meant was "How many ways can 6 letters be posted in 10 letterboxes."
Slots method:
1. 6 slots
2. Each slot has 10 options (because each letter can be put into any of the 10 boxes)
10 10 10 10 10 10
10^6 would be the answer there!
-t
You just asked the same question!
What you may have meant was "How many ways can 6 letters be posted in 10 letterboxes."
Slots method:
1. 6 slots
2. Each slot has 10 options (because each letter can be put into any of the 10 boxes)
10 10 10 10 10 10
10^6 would be the answer there!
-t
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I thought that my question asks about the number of ways for the post box to receive. But your answer is the number of ways for postcards to be posted.
Will it be like, a postbox can receive 10/9/8/7/6/5/4/3/2/1/0 postcards - 11 ways ?
Is this approach totally wrong ?
Will it be like, a postbox can receive 10/9/8/7/6/5/4/3/2/1/0 postcards - 11 ways ?
Is this approach totally wrong ?
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Hey Gughan,
Perhaps I'm misunderstanding you, but I don't see any way in which it's different for letterboxes to receive mail than to send it.
-t
Perhaps I'm misunderstanding you, but I don't see any way in which it's different for letterboxes to receive mail than to send it.
-t
Tommy Wallach, Company Expert
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Thanx Tom !
My question was a weird one ! I know that Anyway, I fully understood your slots method. It 'll be very handy with combinatorics ! Hope this post helps others too...
Cheers,
Gughan Bose
My question was a weird one ! I know that Anyway, I fully understood your slots method. It 'll be very handy with combinatorics ! Hope this post helps others too...
Cheers,
Gughan Bose