A

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?
\(18\)
\(\frac{18!} {3!\, 15!}=816\)
\(18\cdot 16\cdot 3=864\)
\(20\cdot 19\cdot 18=6\:840\)

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?
\(\frac{18!} {3!\, 15!}\)
\(18\)
\(18\cdot 16\cdot 3\)
\(20\cdot 19\cdot 18\)

9000139703

Level: 
A
The box contains \(5\) red crayons, \(4\) yellow crayons and \(2\) green crayons. The crayons are removed from the box and arranged in a line. How many different color patterns can be obtained by this procedure?
\(\frac{11!} {5!\, 4!\, 2!}=6\:930\)
\(5\cdot 4\cdot 2=40\)
\(5!\, 4!\, 2!=5\:760\)
\(\left (5!\, 4!\right )^{2}=8\:294\:400\)

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?
\(36^{4}=1\:679\:616\)
\(10\cdot 26^{4}=4\:569\:760\)
\(\frac{36!} {32!\, 4!}=58\:905\)
\(\frac{26!} {22!\, 4!}=14\:950\)

9000139303

Level: 
A
A DJ's playlist contains \(18\) songs. In this list there are \(7\) rap songs, \(5\) oldies and \(6\) rock songs. The opening part should consist of one rap song, two oldies and one rock song. The order of the songs does not matter. Find the number of possible ways how to put the opening together.
\(420\)
\(120\)
\(320\)
\(520\)

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.
\(22\%\)
\(23\%\)
\(25\%\)
\(50\%\)