Combinatorics

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

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.
\(420\)
\(120\)
\(320\)
\(520\)

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

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).
\(\frac{15!} {9!} =3\:603\:600\)
\(6^{15}=470\:184\:984\:576\)
\(15!\, 6!=941\:525\:544\:960\:000\)
\(\frac{15!} {9!\, 6!}=5\:005\)