Summary Count Of Numbers In Table

I inherited a spreadsheet with a table which summarizes counts based on values in columns from another sheet. For example:

BrownWhiteMulti
Dog326
Cat65
Fish479

The numbers are derived from the second sheet, which displays 1 in Col P for every value of Dog in Col B, 1 in Col Q for every value of Brown in Col C, etc. Col A contains the names of animals. So, in the above matrix the formula for Brown Dog is sum of all 1s in Col P + 1s in Col Q. In another sheet, I would have like Brown Dog in row 1 with all the names of brown dogs going across the column, Brown Cat in row 2 with the names next to it, showing the details behind each number.