Help asap please: How many ternary strings of length n have at least four 0s?
How many bit strings of length 10 have... (a) Exactly four 1s in a row? (b) at least eight 0s in a row?
) Find a recurrence relation for the number of ternary strings of length n≥1 that do not contain two or more consecutive 2s. (Hint: A ternary string consists of 0s, 1s, and 2s.)
Discrete mathematics
2) Let be eumber of ternary strings (of 0s, 1s and 2s) of length n that have no adjacent even digits. For example, so (the empty string), s3 (the strings 0, 1 and 2), while s2 5: 01, 0, 12, 2 because the strings 00,02, 20, 22 are not allowed, as they have adjacent even digits. As another example, the string 10112 is allowed, while the strings 10012 and 120121 are not allowed (a) Find #3; (b) find...
Let n be an even number. How many ternary strings (i.e. strings over the alphabet 10, 1,2]) of length n are there in which the only places that zeroes can appear are in the odd-numbered positions?
consider all bit strings of length 12 How many have 8 0s and 4 1s that have exactly 3 consecutive 1s (allow 4 consecutive 1s)? A 90 В 72 С 45 D 36 E 9
consider all bit strings of length 12 How many have 8 0s and 4 1s that have exactly 3 consecutive 1s (allow 4 consecutive 1s)? A 90 В 72 С 45 D 36 E 9
explain why the recurrence relation for number of ternary strings
of length n contains "01"
7. (10 points) Extra credit: Explain why the recurrence relation for number of ternary strings of length n that contain "01" is bn = 3n-1-bn-2 +31-2?
Exercise 8.12.20: Counting binary strings. (a) How many binary strings of length 12 do not have exactly four 1's? (b) How many binary strings of length 12 start with 101 or 1110? (e) How many binary strings of length 12 start with 00 or end with 00 or both?
Consider all bit strings of length 12. How many have exactly four 1's?
How many binary sequences of length 20 are there that(a) Start with a run of 0s—that is, a consecutive sequence of (at least) one 0—then a run of 1s, then a run of 0s, then a run of 1s, and finally finish with a run of 0s?(b) Repeat part (a) with the constraint that each run is of length at least 2.
Give a recursive formula for the function g(n) that counts the number of ternary strings of length n that do not contain 2002 as a substring. You do not need to find a closed form solution for g(n).