15B Weekly Quizzes
Fall 2001
You may leave sums, products, factorials, binomial coeﬃcients, and so on in your answers.
Q1. A family has 3 girls and 3 boys.
Give reasons for your answers.
(a) How many ways can they sit around a circular table?
(b) How many ways can they sit in a row if girls and boys must alternate; that is, two
boys cannot sit next to each other and two girls cannot sit next to each other?
Q2. Homework problems CL3.1 (3 pair in 6 cards) and CL3.2 (straight).
Q3. Let
A
=
{
1
,
2
,
3
}
and
B
=
{
1
,
2
,
3
,
4
,
5
}
. A function is chosen uniformly at random
from
B
A
.
(a) What is the probability that it is an injection?
(b) What is the probability that it is a surjection?
To receive credit, be sure to show how you got your answers.
Q4. Here is a permutation
f
in cycle form:
(1
,
6
,
3
,
2) (4
,
7
,
5).
(a) Write
f
in oneline form.
(b) Write
f

1
in cycle form.
(c) Write
f
13
in cycle form.
Q5. Given that
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '01
 Bender
 Math, Factorials, Binomial, 2 L, 10 l, 0 1 00 01 1 10 0 L

Click to edit the document details