# 代写MA1510、辅导C++/Java编程

University of Aberdeen
Department of Mathematics
Date 17.02.2023
Code
MA1510 Combinatorics
Assignment 1 >Deadline for submission is 23pm Friday February 24, 2023. Please submit it on My
Aberdeen. 20 Points in total.
result in the loss of marks.
Let A be a set with 9 elements. How many odd size subsets does A have? [3 marks]1.
Use induction to prove that 17n ? 17 is divisible by 4 for all n ∈ N. [5 marks]2.
Define f, g : N→ R by f(n) = n4 + 2 and g(n) = 3n3 · cos(n4 + 1).3.
a) Prove that g(n) = O(f(n)). [2 marks]
b) Prove that f(n) 6= O(g(n)). [3 marks]
4.
a) Compute the binomial coefficient. Justify and explain your answer. [1 mark]
b) Let n ≥ 2. Show that the number of 2-subsets of an n-element set is equal to n(n 1)2.
[1 mark]
c) Suppose you have two boxes. The first box has 9 distinguishable fruits and the
second has 7 distinguishable sandwiches. Suppose you want to take 6 fruits and 3
sandwiches from these boxes for a hike. How many choices do you have? You can leave
the answer in terms of binomial coefficients. [5 marks]