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Default how to find the sum of certain values in a column.

I want to be able to find the sum of all values in a column that have a
particular value in the previous column, sush as follows.

A B
1 TYPE VALUE
2 a 10
3 b 10
4 a 10
5 c 10
6 b 10
7 a 10
8 c 10
9 b 10
10 c 10
11 a 10
12 TOTAL 100

I'm able to total the column fine but what I want is the following:

A) I want is a formula that will total only those VALUES that are TYPE "a"
so that I can multiply the sum by a factor of Y. In this case the answer
would be 40(Y).

B) And I want a different formula that will total those VALUES that are
either TYPE "b" or "c" so that I can multiply the sum by a factor of Z. In
this case the answer would be 60(Z).

Any help would be greatly appreciated.
Thank you.
 
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