Combinatorics

2010007102

Level: 
B
Consider a set of \(n\) mutually different objects. If \(n\) is increased by \(5\), the number of \(2\)-permutations of these objects is increased by \(340\). Find \(n\). (The term „\(k\)-permutation” stands for an ordered arrangement of \(k\) objects from a set of \(n\) objects.)
\( 32\)
\( 34\)
\( 64\)
\( 18\)

2010007103

Level: 
B
Assuming \(x\in \mathbb{N}\), \(n\geq 2\), find the solution set of the following inequality. \[ \left({ x\above 0.0pt x - 2}\right)\cdot \left({x\above 0.0pt 2}\right) - 20\cdot \left({x\above 0.0pt 2}\right) + 96 < 0 \]
\(\{5\}\)
\(\{9;10;11\}\)
solution does not exist
\( (8;12)\)

9000136901

Level: 
B
The sum \(\left({15\above 0.0pt 8} \right) +\left ({15\above 0.0pt 9} \right)\) equals to:
\(\left({16\above 0.0pt 9} \right)\)
\(\left({15\above 0.0pt 10}\right)\)
\(\left({15\above 0.0pt 7} \right)\)
\(\left({16\above 0.0pt 8} \right)\)
\(\left({30\above 0.0pt 17}\right)\)

9000136903

Level: 
B
Simplify \(\left({4\above 0.0pt 0}\right) +\left ({4\above 0.0pt 1}\right) +\left ({4\above 0.0pt 2}\right) +\left ({4\above 0.0pt 3}\right) +\left ({4\above 0.0pt 4}\right)\).
\(4^{2}\)
\(14\)
\(\left({5\above 0.0pt 4}\right)\)
\(32\)
\(\left({8\above 0.0pt 4}\right)\)