Assignment #7
Fully explain your answers for all questions.
1. Find expressions for each of the following. (Leave your answer as a mathematical expression rather than a number.)
(a) The number of ternary strings (strings of 0s, 1s and 2s) of length 9.
(b) The number of strings of 6 lower case letters (a–z) that do no contain any letter twice or more.
(c) The number of binary strings of length 100 that contain at most two 1s.
(d) The number of ternary strings of length 10 (strings of 0s, 1s and 2s) containing exactly two 1s and exactly three 2s.
• Each student is on at least one of these teams and no student is on all four teams.
• Only one student, Hawa, is on three of the teams: she plays chess, netball and soccer.
• There is exactly 1 student who plays basketball and chess.
• There is exactly 1 student who plays basketball and netball.
• Hawa is the only student who plays chess and netball.
• There are exactly 3 students (including Hawa) who play chess and soccer.
• There are exactly 5 students (including Hawa) who play netball and soccer How many students play basketball and soccer?
3. What is the coefficient of x10 in the expansion of (5x2 + 3)14? (Leave your answer as a mathematical expression rather than a number.)
