COUNTIF Like Function with more than 1 Condition

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Hello,

Please help with the following problem:

I want to count the number of cells in a column containing specific text. COUNTIF works great with the condition that it equal that particuar word. But what if I have several conditions?

Ex:

Category1 Category2 Category3 Category4

Furniture Kitchen Chairs Wooden
Furniture Living Room Chairs Wooden
Furniture Kitchen Chairs Wooden
Furniture Living Room Chairs Wooden
Appliances Kitchen Stoves Electric


I want to count the number of each category within Categoties 1, 2, 3 and 4. (I.E., Furniture - 4; Furniture, Kitchen,Chairs, Wooden - 2; etc.)

To count categories within category 1, I can simply use the countif function. But I cannot use the countif function for the other categories. If I count the number of times "Kitchen" appears in Category 2, I will get 3. But I need a condition to count the number of times "Kitchen" appears next to "Furniture." Similarly, the number of times "Chairs" appears next to "Kitchen" and also appears next to "Furniture." Similarly, the number of times "Wooden" appears next to "Chairs" and next to "Living Room" and appears next to "Furniture." And so on. In other words, I want to count the totals for each sub-category.

Is there a similar function to the countif function that I can apply to the above conditions? Can you please show me how it's used in the above example?

Thanks in advance for assisting me in the above problem.
 

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