# Using inclusion-exclusion principle (or otherwise), calculate the exact number of decimal strings

Using inclusion-exclusion principle (or otherwise), calculate the exact number of decimal strings

Question 1

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Suppose that we consider all 10-digit decimal strings  for which  and . Any number of decimals at the start of the string are allowed to be 0. IMPORTANT: For the remainder of the question, ‘a decimal string’ will refer only to the aforementioned sequences of digits

(g) Using inclusion-exclusion principle (or otherwise), calculate the exact number of decimal strings. As part of your solution, you may cite any results from the lectures regarding ‘the number of codewords with k fixed elements’, without proof. Are there enough decimal strings to assign a distinct one for each USA citizen?

Question 2

Question 3

Showing all logical steps, apply Reed decoding to RM (1, 4) to decode the received message 0100011101101110.