9000153804
Level:
A
Find the number of \(3\)-combinations
from the set \(\{2,3,4,5\}\).
\(4\)
\(6\)
\(24\)
\(20\)
Combinatorics
9000153805
Level:
A
Find the number of \(3\)-combinations
with repetition from the set \(\{2,3,4,5\}\).
\(20\)
\(4\)
\(24\)
\(12\)
9000153903
Level:
C
Find the number of ways how to distribute
\(8\) mutually different
balls among \(5\)
persons.
\(5^{8} = 390625\)
\(\frac{8!}
{3!} = 6720\)
\(8^{5} = 32768\)
\(\left({12\above 0.0pt
8} \right) = 495\)
9000153810
Level:
A
Find the number of positive integers with three mutually different digits which can be written just
using the digits \(2\),
\(3\),
\(4\),
\(5\) and which can
be divided by \(3\).
\(12\)
\(6\)
\(9\)
\(10\)
9000153809
Level:
A
Find the number of positive integers with three mutually different digits which can be written just
using the digits \(2\),
\(3\),
\(4\),
\(5\) and which can
be divided by \(4\).
\(6\)
\(9\)
\(10\)
\(5\)
9000148907
Level:
A
A bowl contains \(12\) different
gummy-bears and \(20\)
different sweet-drops. Anne can choose either one sweet-drop or one gummy-bear.
From the rest, Jane can choose one sweet-drop and two gummy-bears. Anne wants to
provide a maximum of the possibilities for Jane's choice. What should Anne choose?
sweet-drop
gummy-bear
Both possibilities give the same result.
9000148908
Level:
A
There are seven different yellow apples, eight different green apples and ten different
red apples. How many ways are there to choose three apples, if we wish to have three
apples of different colors?
\(10\cdot 8\cdot 7=560\)
\(\frac{10\cdot 8\cdot 7}
{2}=280 \)
\((10 + 8 + 7)\cdot 2=50\)
\(10 + 8 + 7=25\)
9000148902
Level:
A
There are four paths from a city to the top of nearby mountain. Find the number of
possible treks from the city to the mountain and back, if it is required to use one
path up and another one down.
\(4\cdot 3=12\)
\(4\cdot 4=16\)
\(4 + 3=7\)
\(2\cdot 4=8\)
9000148909
Level:
A
There are \(24\)
girls and \(8\)
boys in the class. How many ways are there to designate a president and vice-president
of the class if it is required that one of the position will be held by a boy and the
other one by a girl?
\(24\cdot 8\cdot 2=384\)
\(24\cdot 8=192\)
\(\frac{32!}
{2!\; 30!}=496\)
\(\frac{32!}
{24!\; 8!}=10\:518\:300\)
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?
\(4\cdot 4=16\)
\(4!=24\)
\(4\cdot 2=8\)
\(4 + 2=6\)