C

9000153906

Level: 
C
Find the number of ways how to distribute \(5\) identical balls among \(8\) persons so that no persons gets more than one ball.
\(\frac{8!} {5!3!} = 56\)
\(\frac{8!} {3!} = 6\:720\)
\(\left({12\above 0.0pt 8} \right) = 495\)
\(\left({12\above 0.0pt 5} \right) = 792\)

9000154801

Level: 
C
There are six money transports through the Sherwood forest. Robin Hood knows that two of the transports are secured by soldiers. Find the respective probabilities that if Robin's band attacks two random transports, then none, one and both transports will be secured by the soldiers.
\(\frac{6} {15};\, \frac{8} {15};\, \frac{1} {15}\)
\(\frac{3} {9};\, \frac{5} {9};\, \frac{1} {9}\)
\(\frac{1} {3};\, \frac{2} {3};\, \frac{2} {3}\)
\(\frac{1} {2};\, \frac{1} {4};\, \frac{1} {4}\)

9000154804

Level: 
C
Robin Hood wants to have \(6\) children with his love Maid Marian. Find the probability that they will have \(2\) girls and \(4\) boys. The probability that one child will be a girl is \(48.79\%\) and the probability of a boy is \(51.21\%\). Round your answer to three decimal places.
\(0.246\)
\(0.222\)
\(0.015\)
\(0.016\)

9000154805

Level: 
C
A boy plays Monopoly game. He is in the jail and has to roll three times a pair of dices. To escape from the jail he needs the number six on both dices. Find the probability that he succeeds to escape the jail. Round your answer to three decimal places.
\(0.081\)
\(0.919\)
\(0.028\)
\(0.095\)

9000154802

Level: 
C
Three hundred soldiers know details related to the weapon transport to Nottingham. The probability that a soldier betrays the sheriff and tells the details to Robin Hood is \(0.01\) . This probability is fixed for all soldiers. Robin tries to find out the details on the transport by asking each soldier. Find the probability that Robin will find out details (i.e. at least one soldier tells the secret to Robin). Round your answer to three decimal places.
\(0.951\)
\(0.049\)
\(0.827\)
\(0.173\)

9000150505

Level: 
C
The iron support has the shape of the right triangle \(ABC\) with the side \(AB\) of the length \(30\, \mathrm{cm}\) and the hypotenuse \(AC\) of the length \(50\, \mathrm{cm}\) (see the picture). The maximal allowed force \(F_{1}\) on \(AB\) is \(270\, \mathrm{N}\). Find the maximal force \(G\) allowed at the point \(A\). Hint: The load \(G\) at the point \(A\) can be decomposed to the direction of the hypotenuse and the other side of the triangle as shown in the picture.
\(360\, \mathrm{N}\)
\(450\, \mathrm{N}\)
\(540\, \mathrm{N}\)
\(162\, \mathrm{N}\)

9000150501

Level: 
C
A man of height \(180\, \mathrm{cm}\) casts a \(200\, \mathrm{cm}\) shadow. At the same moment, a tree of an unknown height casts a \(35\, \mathrm{m}\) shadow. Find the height of the tree.
\(\frac{63} {2} \, \mathrm{m}\)
\(\frac{350} {9} \, \mathrm{m}\)
\(\frac{72} {7} \, \mathrm{m}\)
\(\frac{36} {35}\, \mathrm{m}\)

9000150503

Level: 
C
A pendulum constituted of a rope of the length \(l\) and a body is displaced from it's equilibrium. The force due to gravity on the body \(F_{g} = 20\, \mathrm{N}\). The body is higher by \(h = 10\, \mathrm{cm}\) in the displaced position (comparing to the equilibrium position). The tension in the rope in the displaced position is \(F_{1} = 12\, \mathrm{N}\). Find the length of the rope \(l\). Hint: Using a parallelogram, the force of gravity on the body can be decomposed into a force \(F_{1}\) in the direction of the rope and \(F_{2}\) in the perpendicular direction.
\(25\, \mathrm{cm}\)
\(25\, \mathrm{m}\)
\(6\, \mathrm{cm}\)
\(16\frac{2} {3}\, \mathrm{cm}\)