A website Maths Puzzle Numerical Ability

For all a,b,c≥0 and a+b+c = 3
Prove that (ab^3 + bc^3 + ca^3)(ab+bc+ca) ≤ 16

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For all a,b,c,d>0 a+b+c+d=4
prove (1/a^2) + (1/b^2) + (1/c^2) + (1/d^2) ≥ a^2 + b^2 + c^2 +d^2 odds in favour of a is 5/3.and evens in against for event b is 4/5.then what is probabelity of occuring at least one event.