Question 376606
Flush in hearts:
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There are 13 hearts and we are to choose 5.  That's

13 choose 5

or

13C5 = 1287
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Three jacks and two sevens?
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There are 4 jacks and we are to choose 3

That's 4 choose 3 

or

4C3 = 4

For each of those 4 ways to select the jacks,

there are 4 sevens and we are to choose 2 

That's 4 choose 2

or 

4C2 = 6

We multiply those and get 4*6 = 24 ways.

Edwin</pre>