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Default Count cells containing text, multiple criteria

I have names in A2:A5 (Joe, Jim, Jake Jones, Jeff Johnson) and birthdates in B2:B5(1980, 1980, 1980, 1981). In A1 is the name criteria (eg "Jake"), and in A2 is the birthdate criteria (eg "1980").

I would like to count the number of times a row satisfies both the name and birthdate criteria. In the case of looking for "Jake" and 1980, it would satisfy Jake Jones, 1980 which is in A4 and B4, and therefore return 1.

I'm attempting the formula:
=SUMPRODUCT((A2:10="*"&A1&"*")*(B2:K2=B1))

but the trouble is, I think, trying to use the wildcards in an array function, which apparently is no go. Is there a better way to do this?

Thanks for any help.
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Default Count cells containing text, multiple criteria

Awesome, I did not know about COUNTIFS!! Thanks for the help!
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