Discrete Math Exam #2 study set verified to pass 2026

Discrete Math Exam #2 study set
verified to pass 2026
Let n and k be natural numbers such that k is less than or equal to n. Then, n choose k is... - correct
answer ✔...n!/[(n-k)!k!] = (n falling factorial k)/(k!)



n choose 0 - correct answer ✔1



n choose 1 - correct answer ✔n



n choose n-1 - correct answer ✔n



n choose n - correct answer ✔1



Binomial theorem: Let n be a natural number. Let x and y be real numbers. Then (x+y)^n = ... - correct
answer ✔... the sum of (n choose k)(x^(n-k))(y^k) from k=0 to n.



Pascal's identity: n choose k = ... - correct answer ✔... [(n-1) choose (k-1)] + [(n-1) choose (k)]



Well Ordering Principle - correct answer ✔Every nonempty subset of the natural numbers has a
smallest element



All solutions to a_n = (s)a_(n-1) + t where s doesn't equal 1 have the form... - correct answer ✔a_n =
c_1(s^n) + c_2



Let s_1 and s_2 be numbers and r_1 and r_2 be roots of the equation x^2 - s_1x- s_2 = 0. If r_1≠ r_2,
then every solution to the recurrence relation a_n = s_1(a_n-1) +s_2(a_n-2) takes the form... - correct
answer ✔a_n = c_1(r_1)^n + c_2(r_2)^n