9000153801
Level:
A
Find the number of mutually different triangles such that each side of each triangle
is either \(2\),
\(3\),
\(4\) or
\(5\).
\(17\)
\(14\)
\(20\)
\(16\)
Combinatorics
9000153802
Level:
A
Find the number of mutually different isosceles triangles (at least
two sides are equal) such that each side of each triangle is either
\(2\),
\(3\),
\(4\) or
\(5\).
\(14\)
\(16\)
\(17\)
\(24\)
9000153803
Level:
A
Find the number of mutually different triangles such that all
three sides of each triangle are mutually different and each side is
\(2\),
\(3\),
\(4\) or
\(5\).
\(3\)
\(4\)
\(14\)
\(16\)
9000153806
Level:
A
Determine the number of three-digit positive integers that can be formed using the digits \(2\),
\(3\),
\(4\) and
\(5\). The digits can be used repeatedly.
\(64\)
\(24\)
\(256\)
\(81\)
9000153808
Level:
A
Find the number of subsets of the set
\(\{2,3,4,5\}\).
\(16\)
\(4\)
\(6\)
\(15\)
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.
\(8^{5} = 32\:768\)
\(\left({12\above 0.0pt
5} \right) = 792\)
\(\frac{8!}
{3!} = 6\:720\)
\(\frac{8!}
{5!3!} = 56\)