Course name: Combinatorics

UVU ++++ - 01001 5. (a) How many 11 digit ternary (characters 0, 1, 2) strings are there where a 2 cannot be followed by a 1? (b) How many 11 digit decimal strings (characters 0 through 9) are there where all the digits add up to less than 98? (c) How many 2n digit binary (characters 0, 1) strings are there where the first n and last n digits both have the same number of occurrences of the number 1? (d) How many permutations (of subsets) of the characters {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} are there so that each permu- tation has the same length as the first digit. UVU ++++ - 01001 5. (a) How many 11 digit ternary (characters 0, 1, 2) strings are there where a 2 cannot be followed by a 1? (b) How many 11 digit decimal strings (characters 0 through 9) are there where all the digits add up to less than 98? (c) How many 2n digit binary (characters 0, 1) strings are there where the first n and last n digits both have the same number of occurrences of the number 1? (d) How many permutations (of subsets) of the characters {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} are there so that each permu- tation has the same length as the first digit