Write a program to print all Armstrong numbers and Prime Numbers in the range inputted by the user. Also print the total count of Prime Numbers in the given range.

Sure, here is a Python program that does that:

def is_prime(n):
    if n <= 1:
        return False
    if n == 2:
        return True
    if n % 2 == 0:
        return False
    i = 3
    while i * i <= n:
        if n % i == 0:
            return False
        i += 2
    return True

def is_armstrong(n):
    num = n
    result = 0
    n = len(str(n))
    while(num != 0):
        digit = num % 10
        result = result + digit ** n
        num = num//10
    return result

start = int(input("Enter the start of the range: "))
end = int(input("Enter the end of the range: "))

prime_count = 0
print("Prime numbers in the given range are: ")
for i in range(start, end+1):
    if is_prime(i):
        print(i, end=" ")
        prime_count += 1

print("\nArmstrong numbers in the given range are: ")
for i in range(start, end+1):
    if i == is_armstrong(i):
        print(i, end=" ")

print("\nTotal count of prime numbers in the given range is: ", prime_count)

This program first defines two helper functions is_prime and is_armstrong to check if a number is prime and Armstrong respectively. Then it takes the start and end of the range as input from the user. It then iterates over the range and checks each number if it's prime or Armstrong using the helper functions and prints them. It also keeps a count of the prime numbers and prints it at the end.