Combinatorics | Number Theory Answers

Combination formulas

Regular plate numbers in the Philippines consist of 3 letters followed by three digits from 0 to 9. How many different license plate numbers with different letters and different digits are there having T as the first letter?

What’s the divisibility of 6 798 340

Determine the digit 100 places to the right of the decimal point in the decimal representation 7/27. (Apply Polya’s Strategy)

What is the largest three digit number that you can make if you use 20 stripes?

You intercept the message "KVW?TA!KJB?FVR."(The blanks after? and R are part of the message,but the final is not.You know that a linear enciphering transformation is being used with a 30- letter alphabet, in which A-Z have numerical equivalents 0-25, blank=26, ?=27, !=28, .=29.You further know that the first six letters of the plain text are "C.I.A". Find the deciphering matrix A inverse and the full plain text message.

Question

A 33​-term series is written using only the integers +9 and −2. How many such series can be written that have a sum of​0?

Answer

The number of series that can be written is 1 107 568.

Request and Details

Can you please provide a process for solving this question? It may involve permutations and combinations.

1.1 On which very old object does a table of prime numbers appear? 

Number of ways an animal can travel from A to C via B, if there are 3 routes from A to B and 5 routes from B to C

with the aid of an example, explain how even and odd parity work and give an example application where they may be useful.