MAS 111 FOUNDATION OF MATHEMATICS
QUIZ 2 HINTS
1. Let A = cfw_1, 2, 3, , 15.
(25 marks)
(a) How many subsets of A contain all of the odd integers in A? (b) How many 10-element subsets of A contain exactly four odd integers? HINTS: (a) Let E = cfw_1, 3, 5,

Nanyang Technological University
Mid-Term Test 2009 MAS 111 Foundations of Mathematics
Time Allowed: 1 Hour
Instructions to the candidates
The examination consists of FIVE (5) problems. Answer all questions. The marks for each question are indicated at t

Nanyang Technological University
Mid-Term Test 2009 MAS 111 Foundations of Mathematics
Hints
Instructions to the candidates
The examination consists of FIVE (5) problems. Answer all questions. The marks for each question are indicated at the end of each

Nanyang Technological University
Mid-Term Test 2009 2 MAS 111 Foundations of Mathematics
Time Allowed: 1 Hour
Instructions to the candidates
The examination consists of FIVE (5) problems, each of which is of 20 marks. Answer all questions. The marks for

Polyas Enumeration Theorem
F. Oggier
August 10, 2016
These notes have been made using the following references [1, 2, 3, 4].
1
Counting Necklaces
Consider a decorative ornament that consists of n coloured bead, arranged on
a circular loop of strings. This