CALCULATION OF NUMERICAL SEQUENCES AND THEIR SUMS ARISING IN THE PROCESS OF SOLVING SOME PROBLEMS OF COMBINATORICS
Keywords:
topology, three-digit numbers, method, case, letters.Abstract
Issue 1. How many words can be formed without two o's next to each other by swapping the letters in the word topology?
Solving. The word "topology" is a 10-letter word with 3 letters "o" and the rest of the letters are different. We number the places where the letters in the word topology should be located. For convenience, we replace the number 10 with the number a.
The letters in the word topology are placed in positions 1, 2, 3, 4, 5, 6, 7, 8, 9, a. We express each different option in the form of three-digit numbers in the following way: if the letters o are located in positions 1,2,3, the number 123 is formed, if the letters o are located in positions 5,7,9 if there is, the number 579 is formed. We need to calculate the number of three-digit numbers whose digits are not consecutive numbers that can be formed by the method described above, according to the condition of the problem. First, we count the number of numbers whose first digit is 1.
