Letters

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?


The answer is 1220703125.

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3 solutions

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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

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

Samuel Li - 6 years, 4 months ago

I wonder why is this question at level 4 =.=

Arya Haldar - 6 years, 9 months ago

Are you sure this is correct? Using stars and bars gives a totally different answer....

Kartik Prabhu - 6 years, 11 months ago

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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?

Kartik Prabhu - 6 years, 11 months ago

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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.

Calvin Lin Staff - 6 years, 11 months ago

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@Calvin Lin Understood. Thanks Calvin!

Kartik Prabhu - 6 years, 11 months ago

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@Kartik Prabhu What is stars and bars rule ... when we can apply that rule .. ??

anmol garg - 6 years, 10 months ago

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@Anmol Garg Even I want to know that...!!!

Mohit Khanwale - 6 years, 4 months ago

@Calvin Lin if the letters are indistinguishable is the answer 173485?

Arnab Bhattacharya - 6 years, 9 months ago
Sayan Tapadar
Sep 22, 2017

Each letter can be posted in 5 different postboxes.There are 13 letters so by rule of product no. Of ways = 5^13

Mukhar Jain
Feb 28, 2015

We can say that the letters are small and hense can be dispersed and not the postboxes there for 5 13 5^{13} = the ans

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