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5. Binomial Coefficients (a) How many subsets with at least 5 elements does a set with 8 elements have? n+3 (b). Fi...
Binomial Coefficients (a). How many subsets with at least 5 elements does a set with 8 elements have? (b). Find the coefficient of r" in (3 - 2.0)"+3. (c). How many ways are there to walk down from the top of Pascal's Triangle and end somewhere on the number 20?
Show your work, please 5. Binomial Coefficients (a). How many subsets with at least 5 elements does a set with 8 elements have? (b). Find the coefficient of 2" in (3 - 2.c)"+3 (c). How many ways are there to walk down from the top of Pascal's Triangle and end somewhere on the number 20?
If a given set has thirteen elements, how many of its subsets have somewhere from four through eight elements?
2. Given the set S-ta,b,c,d,e,f,g,h) a) How many subsets does S have? b) How many subsets have exactly 5 elements? c) A subset is randomly chosen for the collection of all possible a) b) c) subsets. What is the probability that it contains exactly 3 elements? d) A subset is chosen at random from all the subsets. d) What is the probability that it contains the element a?
Block Walking and Counting Subsets Recall that a standard deck has 52 cards in it. (a). The number of 5-card hands corresponds to what entry in Pascal's Triangle? (b). The number of 7-card hands matches the number of (Right, Up)-paths from 0,0) to what point in the first quadrant? (c). For parts (a) and (b) above, find a term y in an appropriate binomial expansion (x + y)" whose coefficient matches your answer. (d). How many 51-card hands are there?...
1. A universal set, with n(U)70, is partitioned into three subsets: A, B, and C. If n(B) 3-n(A), and n(C) 2-n(B), find the number of elements in the subset A. 2. A license plate consists of eight symbols on each plate, where the first three symbols are letters of the alphabet and the following five symbols are the digits selected from the set f0, 1, 2, 3, 4, 5, 6, 7, 8, 9)? How many license plates can be produced...
41. How many subsets does the set {a, b, c, d, e,f} have?
1. Let U be the universal set with disjoint subsets A and B, where n(U-46, n(A-15, and n(B-14. Find nAn B 2. A merchant surveyed 300 people to determine the way they leaned about an upcoming sale. The survey showed that 180 learned about the sale from the radio, 170 from television, 130 from the newspaper, 120 from radio and television, 70 from radio and newspapers, 80 from television and newspapers, and 60 from all three sources. How many people...
Timelimit Total Points Possible: 19 How many subsets does the set D = {c, a, t} have? Questions Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q 13 Points possible: 1 This is attempt 1 of 1 Submit Q14 Q15 Q16 Q17 Q 18 Q19 Print Version 44 11 Feo F10 % & 2 3 4 7 9 W R E T Y U P O * CO est Timelimit: 1 hour, 15 minutes. 1: Which...
Set 5 a. A staircase has 10 steps. You walk up taking one or two at a time. How many ways can you go up? We have n dollars to spend. Every day we either buy a candy for 1 dollar, or an ice cream for 2 dollars. In how many ways can we spend the money? Explain for n-5, and then conjecture for n dollars. Prove your conjecture. Define Fibonacci numbers completely. Why do you need two initial values?...