2010007106
Level:
A
Determine the number of four-digit positive integers that can be formed using the digits \(0\), \(1\), \(2\), \(3\), \(4\). The digits can be used repeatedly.
\( 500 \)
\( 96 \)
\( 625 \)
\( 120 \)
Combinatorics
2010007601
Level:
A
How many ways are there to arrange the letters in the Czech word LOKOMOTIVA?
\( \frac{10!}{3!} \)
\( \frac{10!}{3} \)
\( \frac{10!}{2!} \)
\( 10!\)
2010007606
Level:
A
In how many ways can a four-person team be selected from a group of \(10\) students?
\(\frac{10!}
{4!\; 6!}\)
\(\frac{10!}
{4!}\)
\(\frac{10!}
{ 6!}\)
\(10!\)
9000139301
Level:
A
Five different pieces of fruit are there on the plate. In how many ways it is possible
to distribute them into five children, if each child should have one piece?
\(120\)
\(100\)
\(140\)
\(160\)
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?
\(120\)
\(320\)
\(520\)
\(720\)
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.
\(420\)
\(120\)
\(320\)
\(520\)
9000139304
Level:
A
Find the number of possibilities how to choose a pair of timekeepers for a sport event if
there are \(50\)
candidates available for this job.
\(\frac{50!}
{2!\; 48!} = 1\:225\)
\(\frac{50}
{2} = 25\)
\(50^{2} = 2\:500\)
\(\frac{50!}
{48!} = 2\:450\)
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.
\(\frac{20!}
{5!\; 15!}=15\:504\)
\(20\cdot 3\cdot 5=300\)
\(\frac{20!}
{3!\; 5!}=3\:379\:030\:566\:912\:000\)
\(20^{5}=3\:200\:000\)
9000139306
Level:
A
How many different ice cream bowls can be prepared from
\(8\) kinds
of an ice cream if the bowl contains just three different kinds of ice cream?
\(\frac{8!}
{3!\; 5!}=56\)
\(\frac{8!}
{2!\; 5!}=168\)
\(\frac{8!}
{5!}=336\)
\(8!=40\:320\)
9000139307
Level:
A
There are \(10\)
students hurrying to the dining room. Find the number of possibilities how can be
these students ordered into the row to get the meal.
\(10!=3\:628\:800\)
\(10\)
\(10^{10}\)
\(\frac{10!}
{10} =362\:880\)