Math Is Fun Forum

chetah

Member

Registered: 2008-02-15

Posts: 32

Discrete Math

An alphabet of 40 symbols is used for transmitting messages in a communication system.  How many distinct messages (list of symbols) of 25 symbols can the transmitter generate if symbols can be repeated in the message?  How many if 10 of the 40 symbols can appear only as the first and/or last symbols of the message, the other 30 symbols can appear anywhere, and repetitions of all symbols are allowed?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Discrete Math

If it was a message made of only one symbol, then there would be 40 distinct messages.
If it was made of two symbols, then there would be a choice of 40 for the first symbol, and another choice of 40 for the second. So, there would be 40*40 = 1600 distinct messages in total.

Applying the reasoning to a 25-symbol message gives that there are 40^25 ≈ 10^40 distinct messages in all.

For the second problem, you consider the middle 23 symbols separately from the first and last ones, and apply similar reasoning to above to get the answer.

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Why did the vector cross the road?
It wanted to be normal.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Discrete Math

Let's do a test to try this out.
Given 2 symbols, M and O, let's
predict all 3 letter words.
(2)(2)(2) = 8    I multiplied.
MOM
OOO
MMM
MMO
OOM
OMM
MOO
OMO
Try to list them yourself without looking.
How many have 2 O's?
How many have 1 M ?

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