Question 1137515
Using notation nCr = n!/((n-r)!r!)<br>

Form of hand:  aabbc   (where a,b,c represent different RANKS of any suit)<br>

(#ways to draw two a's)*(#ways to draw two b's)*(#ways to draw c)<br>

Notes:  13C2 ways to draw a,b from the 13 ranks
         4C2 ways to arrange rank a (4 suits, 2 chosen)
         4C2 ways to arrange rank b (4 suits, 2 chosen)
        11C1 ways to draw c from the remaining 11 ranks
         4C1 ways to draw c of a given suit<br>

Putting it together:
  13C2*4C2*4C2*11C1*4C1 = 78*6*6*11*4 = {{{highlight(123552)}}} hands

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But, you may ask, why not pick the unmatched card (c) from the 13 ranks first?  Let's try it that way:<br>
       13C1 ways to pick rank c
        4C1 ways to draw c of a given suit
       12C2 ways to pick ranks a,b  <<< note how there are 12 ranks to pick from
        4C2 ways to arrange rank a suits
        4C2 ways to arrange rank b suits <br>

   = 13*4*66*6*6 = 123552, as before