Note: I need typed answers only and your own work please

Question 5: Consider a string of characters of length n where each character is chosen from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. We will call these decimal strings. (a) We call a decimal string (0-free if it does not contain two consecutive O's. Let D,, be the number of 00-free decimal strings of length n. Determine D, and D2, then express Dn in terms of Dn-1 and Dn-2 for n 2 3. 2 (b) Find an expression for the number of 00-free decimal strings of length n with precisely i O's. As in Question 4 there can be at most n - [" | 0's in the string, so you may assume i