Pythonic way to count sequences

[CM]

I have to count the number of various two-digit sequences in a list
such as this:

mylist = [(2,4), (2,4), (3,4), (4,5), (2,1)]  # (Here the (2,4)
sequence appears 2 times.)

and tally up the results, assigning each to a variable.  The inelegant
first pass at this was something like...

# Create names and set them all to 0
alpha = 0
beta = 0
delta = 0
gamma = 0
# etc...

# loop over all the tuple sequences and increment appropriately
for sequence_tuple in list_of_tuples:
    if sequence_tuple == (1,2):
        alpha += 1
    if sequence_tuple == (2,4):
        beta += 1
    if sequence_tuple == (2,5):
        delta +=1
# etc... But I actually have more than 10 sequence types.

# Finally, I need a list created like this:
result_list = [alpha, beta, delta, gamma] #etc...in that order

I can sense there is very likely an elegant/Pythonic way to do this,
and probably with a dict, or possibly with some Python structure I
don't typically use.  Suggestions sought.  Thanks.