The current Czech vehicle registration plate number has the form NLN-NNNN, where N stands
for a digit from
to
and L stands for a letter from an alphabet containing
letters. How many different registration plates are possible?
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.
A combination lock will open if a right choice of three numbers (from
to
) is selected.
Suppose that we use a brute force attack to open the lock (we try all possibilities). To try one
code takes
seconds. What is the maximal time (in seconds) required to open the lock by brute
force?
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?
The king has eight daughters. A dragon asks two daughters, otherwise he will
destroy the whole country. In how many ways can we choose a pair of king's
daughters for the dragon?
A bowl contains different
gummy-bears and
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?
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?
There are
girls and
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?
The player throws a dice in a desktop game. If he gets the number
, he
throws again and his score is the sum of both numbers. Find how many possibilities
are there for the player's score.