Let A be the set of five-digit numbers where only the digits 1, 2 and 3 are included. For example 12331, 23211 and 32223 will be included in A. a)How many numbers in A does the digit 1 contain exactly...

Let A be the set of five-digit numbers where only
the digits 1, 2 and 3 are included. For example
12331, 23211 and 32223 will be included in A.

a)How many numbers in A does the digit 1 contain
exactly twice?

b)How many numbers in A do not have two 1s next
to each other? For example, have
32113 and 31112 two 1s next to each other, but it
does not have 13122, 12121
and 23232.

c)How many numbers in A are there that have a
cross sum equal to 10? This applies, for example
the numbers 31231 and 32122, but not 32123.