Question 1144466
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Empirically (by looking at examples) the given expression is equivalent to (n+3)Cr.  e.g....<br>
6C3+3*6C4+3*6C5+6C6 = 20+3(15)+3(6)+1 = 84 = 9C6
5C1+3*5C2+3*5C3+5C4 = 5+3(10)+3(10)+5 = 70 = 8C4
7C2+3*7C3+3*7C4+7C5 = 21+3(35)+3(35)+21 = 252 = 10C5<br>
Proving it algebraically looks like a nightmare, unless there is some trick I don't see.