Discrete Mathematics Assignment-6

a)
b)
c)

There are only 3 situations z=2,1,0
when then

when then

when then

There are totally 21 ways to pick 10 coins such that the total amount is at most ￥20

a) neither an injection nor a surjection
There are kinds of function
b) is an injection
kinds of function
c) is a surjection
kinds of function
d) is an bijection
=m!/ (m-n)!

c:
d: if n = m The number of bijections from a set A with n elements to a set B with m elements is
if n m The number of bijections from a set A with n elements to a set B with m elements is .

is injection \because |A|>|B| $ If A are placed into B, then there is at least one box containing at least 2 objects.
$\therefore $ It can't be an injection function

Suppose the length of the string is n
is the number of binary strings

and

Suppose that
$ r_2=5\therefore a_n=\alpha_12^n+\alpha_25^na_0=2=\alpha_1+\alpha_2a_1=1=2\alpha_1+5\alpha_2\therefore \alpha_1=3$