* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Permutations and Factorial Notation Worksheet
Survey
Document related concepts
Mechanical calculator wikipedia , lookup
Approximations of π wikipedia , lookup
Abuse of notation wikipedia , lookup
Location arithmetic wikipedia , lookup
Bra–ket notation wikipedia , lookup
Large numbers wikipedia , lookup
Principia Mathematica wikipedia , lookup
History of mathematical notation wikipedia , lookup
Musical notation wikipedia , lookup
Elementary arithmetic wikipedia , lookup
Big O notation wikipedia , lookup
Transcript
Permutations and Factorial Notation Worksheet 1) Evaluate each of the following without a calculator. a) 5! b) 20! 18! c) 10! 9! d) 10 ! 10 9 ! d) ( a 1)! ( a 1)! 2) Simplify each of the following expressions. a) n! ( n 1)! b) (a 1)! (a 2)! c) a! (a 2)! 3) On the assembly line at factory, six digit serial numbers are assigned to products according to the following regulations: only the digits 4 to 9 are used; no digit may be used twice in the same serial number. a) Use the Fundamental Counting Principle to calculate the number of possible serial numbers under the system. b) Write this answer using factorial notation. 4) Express each of the following in factorial notation. a) P(7,7) b) P(m,m) c) P(7,5) d) P(a,b) 5) Solve for n, where n N. a) ( n 1)! 9 n! b) n! 20 (n 2)! 6) List all of the 2-arrangements of the symbols {+, -, x} 7) Determine the following values of n and r in P(n, r) for each of the following. a) b) c) d) P(n, r) = 6 x 5 x 4 x 3 x 2 x 1 P(n, r) = 8 x 7 x 6 P(n, r) = 510 x 509 x 508 x 507 P(n, r) = a (a -1)(a – 2) Answers: 1a) 120 b) 380 c) 10 d) 1 3) 6 x 5 x 4 x 3 x 2 x 1 = 720 b) 6! 5a) 8 b) 5 c) n = 510, r = 4 2a) n 4a) 7! 6) +-, -+, +x, x+, -x, xd) n = a, r = 3 b) a-1 c) a a b) m! c) 2 d) a a 7! a! d) 2! (a b)! 7a) n = 6, r = 6 b) n = 8, r = 3 2