Find the number N of surjective (onto) functions from a
set A to a set B...
Find the number N of surjective (onto) functions from a
set A to a set B where:
(a) |A| = 8, |B| =
3; (b) |A| = 6, |B| =
4; (c) |A| = 5,|B| =
5; (d) |A| = 5, |B| =
7.
If |A| = n and |B| = m, how many functions are there mapping A
to...
If |A| = n and |B| = m, how many functions are there mapping A
to B?
if n > m, How many are one to one?
if n = m, How many are one to one (give your answer in terms of
n)?
if m > n, How many are one to one?
How many ternary strings (strings of elements taken from the
set{0,1,2}) of length2n are there in...
How many ternary strings (strings of elements taken from the
set{0,1,2}) of length2n are there in which the zeroes appear only
in all odd-numbered positions?
How many ternary strings of length 7 will contain at least one
0?
Let S = {a,b,c,d,e,f,g} and let T = {1,2,3,4,5,6,7,8}.
a. How many different functions are there from...
Let S = {a,b,c,d,e,f,g} and let T = {1,2,3,4,5,6,7,8}.
a. How many different functions are there from S to
T?
b. How many different one-to-one functions are there from S to
T?
c. How many different one-to-one functions are there from T to
S?
d. How many different onto functions are there from T to
S?
Using the inclusion-exclusion method, what is the number of
functions f from the set {1,2,...,n} to...
Using the inclusion-exclusion method, what is the number of
functions f from the set {1,2,...,n} to the set
{1,2,...,n} so that f(x)=x for some x
and f is not one-to-one?