From my way to school from house, there are 5 post boxes. My mother gave me 13 (distinct) letters to post. If I can post each letter in any post box I want, in how many ways can I post the letters?
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I thought that the order that the letters were put into a given mailbox didn't matter (i.e. only the content of the mailbox mattered), so I used 17C4. :P
I wonder why is this question at level 4 =.=
Are you sure this is correct? Using stars and bars gives a totally different answer....
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Perhaps you're right - each letter can go in one of 5 post boxes. So there's 5^1 ways to distribute one letter, 5^2 ways to distribute two letters, 5^3 ways to distribute 3 letters... etc. But why doesn't stars and bars work?
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The letters are distinct, which is why you need to use the product rule.
If the letters are indistinguishable, then stars and bars would apply.
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@Calvin Lin – Understood. Thanks Calvin!
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@Kartik Prabhu – What is stars and bars rule ... when we can apply that rule .. ??
@Calvin Lin – if the letters are indistinguishable is the answer 173485?
Each letter can be posted in 5 different postboxes.There are 13 letters so by rule of product no. Of ways = 5^13
We can say that the letters are small and hense can be dispersed and not the postboxes there for 5 1 3 = the ans
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We put letter in the box so, the hand is up and the post box is down. In the similar way 13 is up and 5 is down.
= 5 raise to 13
= 5^13
=1220703125