Web6.3 pg 413 # 11 How many bit strings of length 10 contain a)exactly four 1s? This is just asking us to choose 4 out of 10 slots to place 1’s in. C(10;4) = 10!=(4! 6!) = (10 9 8 7)=4! = 210. b)at most four 1s? We add up the number of bit strings of length 10 that contain zero 1s, one 1, two 1s, three WebDec 20, 2024 · How many \(9\)-bit strings (that is, bit strings of length 9) are there which: Start with the sub-string 101? Explain. ... We can think of each row as a 6-bit string of weight 3 (since of the 6 coins, we require 3 to be pennies). Thus there are \({6 \choose 3} = 20\) rows possible. Each row requires 6 coins, so if we want to make all the rows ...
1.E: Counting (Exercises) - Mathematics LibreTexts
WebDec 18, 2024 · 4. Number of 6-bit strings with weight of 3 is 20. 5. Number of 6-bit strings with weight of 5 is 6. 6. Number of 6-bit strings with weight of 6 is 1. 7. Number of 6-bit … Webkindly answer it perfectly Transcribed Image Text: Recall that a 5-bit string is a bit strings of length 5, and a bit string of weight 3, say, is one with exactly three 1's. How many 5-bit strings are there? How many 5-bit strings have weight 0? How many 5-bit strings have weight 1? How many 5-bit strings have weight 2? pelvic floor breathing
SOLUTION: How many 9-bit strings are there which: a) Start
WebCase 1: Have weight 5. From the 9 places to have digits, there are 5 places to have 1's. That's "9 choose 5" = 9C5 = 126 Case 2: Start with 101 That's problem a), or 64 Case 3. Have weight 5 and start with 101. That's problem b), or 20 Let A = the set of 9-bit strings with weight 5. Let B = the set of 9-bit strings that start with 101. Webc) How many bit strings of length seven contain three consecutive 0s? Let a n denote the number of such strings of length n. a) Consider a string of length n 3 that contains three consecutive 0s. Such a string either ends with 1, or with 10, or with 100, or with 000. In the rst case, there are a n 1 possibilities. In the second case, there are ... pelvic floor disability index