9000153808
Level:
A
Find the number of subsets of the set
\(\{2,3,4,5\}\).
\(16\)
\(4\)
\(6\)
\(15\)
Combinatorics
9000153807
Level:
A
Find the number of the positive integers with three digits which can be written using
the digits \(2\),
\(3\),
\(4\) and
\(5\). Each
digit can be used at most once.
\(24\)
\(64\)
\(256\)
\(81\)
9000153901
Level:
C
Find the number of ways how to distribute
\(8\) identical
balls among \(5\)
persons so that each of them gets at least one ball.
\(\left({7\above 0.0pt
3}\right) = 35\)
\(5^{3} = 125\)
\(\left({12\above 0.0pt
5} \right) = 792\)
\(\left({12\above 0.0pt
8} \right) = 495\)
9000153902
Level:
C
Find the number of ways how to distribute
\(8\) identical
balls among \(5\)
persons.
\(\left({12\above 0.0pt
8} \right) = 495\)
\(5^{8} = 390625\)
\(\left({8\above 0.0pt
5}\right) = 56\)
\(\left({12\above 0.0pt
5} \right) = 792\)
9000153905
Level:
C
Find the number of ways how to distribute
\(5\) identical
balls among \(8\)
persons.
\(\left({12\above 0.0pt
5} \right) = 792\)
\(8^{5} = 32768\)
\(\left({12\above 0.0pt
8} \right) = 495\)
\(\frac{8!}
{3!} = 6720\)
9000153907
Level:
C
Find the number of ways how to distribute
\(5\) different
balls among \(8\)
persons.
\(8^{5} = 32\:768\)
\(\left({12\above 0.0pt
5} \right) = 792\)
\(\frac{8!}
{3!} = 6\:720\)
\(\frac{8!}
{5!3!} = 56\)
9000148904
Level:
A
Pamela needs new ski for a ski course. There are skis from six different vendors in a
shop. The shop has four different ski pairs from each vendor, but two vendors have all
products behind Pam's financial limit. How many pairs are at disposal for Pam?
\(4\cdot 4=16\)
\(4!=24\)
\(4\cdot 2=8\)
\(4 + 2=6\)
9000148910
Level:
A
The player throws a dice in a desktop game. If he gets the number
\(6\), he
throws again and his score is the sum of both numbers. Find how many possibilities
are there for the player's score.
\(5 + 6=11\)
\(2\cdot 6=12\)
\(1 + 6=7\)
\(6\cdot 6=36\)
9000148901
Level:
A
The current Czech vehicle registration plate number has the form NLN-NNNN, where N stands
for a digit from \(0\)
to \(9\)
and L stands for a letter from an alphabet containing
\(26\)
letters. How many different registration plates are possible?
\(26\cdot 10^{6}\)
\(10^{6}\)
\(15\cdot 10^{6} + 6\cdot 10^{5}= 156\cdot 10^{5}\)
\(16\cdot 10^{6}\)
9000148903
Level:
A
A combination lock will open if a right choice of three numbers (from
\(1\) to
\(9\)) is selected.
Suppose that we use a brute force attack to open the lock (we try all possibilities). To try one
code takes \(20\)
seconds. What is the maximal time (in seconds) required to open the lock by brute
force?
\(20\cdot 9^{3}\, \mathrm{s}=14\:580\,\mathrm{s}\)
\(20\cdot \frac{9!}
{6!}\, \mathrm{s}=10\:080\,\mathrm{s}\)
\(20\cdot \frac{9!}
{3!\; 6!}\, \mathrm{s}=1\:680\,\mathrm{s}\)
\(20\cdot 9\cdot 3\, \mathrm{s}=540\,\mathrm{s}\)