Lesson $1\mathrm{.}2$ Permutations

$3)$ The map of a local park is shown below. The dashed lines represent walking paths and stars represent the park$$s

entrance and exit. Assuming you want to walk directly from the park entrance to the park exit, that is you will

NOT retrace any point, how many options are there for you to take your walk? $(10$ points$).$

$4)$ Use the following lines of code to answer their respective questions.

Parts a & b

for i :$=1$ to $5$ do

print i

for j :$=6$ to $10$ do

print j

for k :$=11$ to $15$ do

print k

Parts c & d

for i :$=1$ to $5$ do

for j :$=6$ to $10$ do

for k :$=11$ to $15$ do

print i $+$ j $+$ k

a$.$ Calculate the number of times the print statement is executed? Note that the $$for loops$$ are sequential.

b$.$ What counting principle did you use?

c$.$ Calculate the number of times the print statement is executed? Note that the $$for loops$$ are nested.

d$.$ What counting principle did you use $7)$ The host of a party is distributing candy to the $10$ children in attendance. The host has $20$ chocolate bars and $15$

bags of M&Ms$.(20$ points$)$

a$.$ How many ways can the candy be distributed?

b$.$ If each child is to receive at least one chocolate bar and at least one bag of M&Ms$,$ how many ways can

the candy be distributed $6)$ The owners of a small business purchased $20$ lottery tickets to give to their $5$ employees. $(20$ points$)$

a$.$ How many ways can the lottery tickets be distributed?

b$.$ If each employee is to receive at least two lottery tickets, how many ways can the lottery tickets be

distributed