Question 1054448
There are 13 diamonds and 13 hearts = 26 red cards
The combinations of 5 objects taken from 26 objects is
{{{(26!)/ (5!(26-5)!) }}} 
= {{{(26!)/ (5!(21)!) }}}
= {{{(26*25*24*23*22*(21)!)/ (5!(21)!) }}}
We can now cancel out {{{((21)!)/ (21)!}}}
= {{{(26*25*24*23*22)/5!}}}
= {{{(26*25*24*23*22)/(5*4*3*2*1)}}}
Notice 25 factors to 5*5, 24 factors to 4*3*2 so substituting,
= {{{(26*5*5*4*3*2*23*22)/(5*4*3*2*1)}}}
Simplifying,
= {{{(26*5*23*22)/(1)}}}
= 65780