Calculator or any other electronic devices are NOT allowed. You can give an answer as a formula (e. g. 335) unless the problem states specifically that you have to give a number. Time allotted is 40 minutes. An asterisk marks non-obligatory (bonus) questions.
1) Formulate the addition rule and multiplication rule in your own words
2) What is the number of different passwords of length 5:
a) containing digits only
b) containing digits OR one of 10 characters , . / ? ' " ! * ( )
c) how much the answer in b) is bigger than the answer in a) (you have to give an explicit answer here)
3) Joe wants to throw a party. He has to choose a stuffing for quesadillas out of 3 different ones and a drink out of 5 options (but keep in mind that all of them are non-alcoholic!). In how many ways can he make a choice (please give explicit number)?
4*) Mary is organizing her vacations. She will go to Florida, New York, Califormia, Mexico and Samara, Russia once. In how many ways can she order her destinations (please give explicit number)?
5) Please choose quadratic functions from the following:
a) \( x^2+2x+1 \)
b) \( x^3+2x+1 \)
c) \( (x-1)^2+1 \)
d) \( -(x+0.5)^2-0.1 \)
e) \( (x+10)^3+1 \)
f) \( (x-1)(x-3) \)
g) \( x^2+x+1 \)
h) \( x^2+2x+1 \)
j) \( x+153.5 \)
Out of those which are quadatic functions, choose the ones whose branches look up.