A

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?
\(24\cdot 23=552\)
\(25\cdot 24=600\)
\(24\cdot 23\cdot 22=12\:144\)
\(25\cdot 24\cdot 23=13\:800\)

9000139309

Level: 
A
There are \(20\) tablets in an e-shop. From this amount \(18\) tablets are new and \(2\) tablets have been returned by customers. The e-shop manager gets an order containing three tablets and he wants to get rid of the returned tablets first. How many possibilities exist to complete the order?
\(18\)
\(\frac{18!} {3!\; 15!}=816\)
\(18\cdot 16\cdot 3=864\)
\(20\cdot 19\cdot 18=6\:840\)

9000139509

Level: 
A
The average year income in a company was \(200\: 000\, \mathrm{Euro}\) two years ago. This income increased by \(10\%\) a year ago and by \(80\: 000\, \mathrm{Euro}\) this year. Find the average percentage increase in the average income per one year and round to the nearest percent.
\(22\%\)
\(23\%\)
\(25\%\)
\(50\%\)

9000139310

Level: 
A
There are \(20\) tablets in an e-shop. From this amount \(18\) tablets are new and \(2\) tablets have been returned by customers. The e-shop manager gets an order containing three tablets and he wants to use only the new tablets for this order. How many possibilities exist to complete the order?
\(\frac{18!} {3!\; 15!}\)
\(18\)
\(18\cdot 16\cdot 3\)
\(20\cdot 19\cdot 18\)

9000139510

Level: 
A
The price of a butter increased by \(8\%\) in the year \(2013\) and by \(34\%\) in the year \(2014\). Find the average percentage growth of the price of the butter per one year in the period \(2012\)-\(2014\). Round your answer to the nearest percent.
\(20\%\)
\(21\%\)
\(14\%\)
\(26\%\)

9000139701

Level: 
A
There are \(15\) athletes in an athletic meeting. Determine in how many ways it is possible to obtain the results on the first six places of the scoreboard if the place on scoreboard cannot be shared (one athlete per one place on scoreboard).
\(\frac{15!} {9!} =3\:603\:600\)
\(6^{15}=470\:184\:984\:576\)
\(15!\, 6!=941\:525\:544\:960\:000\)
\(\frac{15!} {9!\, 6!}=5\:005\)