A

9000139305

Level: 
A
There are five rooms with three beds and one room with five beds in a hotel. A group of \(20\) people booked rooms at this hotel. Determine the number of possible choices for the people to the five-bed room.
\(\frac{20!} {5!\; 15!}=15\:504\)
\(20\cdot 3\cdot 5=300\)
\(\frac{20!} {3!\; 5!}=3\:379\:030\:566\:912\:000\)
\(20^{5}=3\:200\:000\)

9000139705

Level: 
A
From the group of \(10\) boys and \(5\) girls we have to select a small group of \(3\) boys and \(2\) girls. How many possibilities exist for this choice?
\(\frac{10!} {7!\, 3!}\cdot \frac{5!} {3!\, 2!}=1\:200\)
\(5^{10}=9\:765\:625\)
\(10\cdot 5!\, 3!=7\:200\)
\(5\cdot \frac{10!} {3!} =3\:024\:000\)

9000139706

Level: 
A
The international alphabet contains \(26\) letters. The letters of this alphabet and the digits from \(0\) to \(9\) are used to form a code of the length \(4\) (a code contains \(4\) characters). The characters may repeat through the code and the code is not case sensitive (uppercase letters are equivalent to lowercase letters). How many codes can be obtained?
\(36^{4}=1\:679\:616\)
\(10\cdot 26^{4}=4\:569\:760\)
\(\frac{36!} {32!\, 4!}=58\:905\)
\(\frac{26!} {22!\, 4!}=14\:950\)

9000139302

Level: 
A
The phone number contains nine digits. A witness does not remember the full number, but he remembers that the phone number starts by \(728\), ends by \(01\) and there is no repeating digit in the number. How many phone numbers meet these conditions?
\(120\)
\(320\)
\(520\)
\(720\)

9000139308

Level: 
A
The shooting club has \(25\) members. Among the members it is necessary to vote a board: a president, a cashier and a webmaster. One person cannot have more than one of these positions and there is only one member skilled enough to be a webmaster. How many possibilities exist to set up the board?
\(24\cdot 23=552\)
\(25\cdot 24=600\)
\(24\cdot 23\cdot 22=12\:144\)
\(25\cdot 24\cdot 23=13\:800\)

9000121709

Level: 
A
Consider a rectangle \(ABCD\) of a special ratio between the length and the width: if \(E\), \(F\), \(G\) and \(H\) denote the midpoints of the sides \(AB\), \(BC\), \(CD\) and \(DA\), respectively, then the measure of the angle \( AEH\) is \(25^{\circ }\). Find the measure of the angle \( EFG\).
\(50^{\circ }\)
\(65^{\circ }\)
\(75^{\circ }\)
\(130^{\circ }\)