Question 1:   How many four-digit numbers can you get out of $0, 3, 7, 8$ ?

Question 2:   There are $19$ balls in the box: $10$ of red ones and $9$ of blue ones. In how many ways can two balls of the same color be picked?

Question 3:   In how many ways can you pick a captain and his deputy in a group of $23$ soldiers?

Question 4:   John has $4$ cats. In how many ways he can take $2$ of them in his hands (one - in left hand, another - in right)?

Question 5:   Three passengers walk into the elevator of the $11$-floor building (ground floor is not included). In how many ways all three passengers can get out on different floors?

Question 6:   From the box in which there are $10$ white, $4$ red and $5$ green balls, are randomly picked $3$ . What is the probability that all three of them would be white?

Question 7:   The situation is the same as in the previous task. What is the probability of picking one white, one red and one green ball?

Question 8:   At the language school people can only study French, German or both. The event $A$ happens when a random student decides to study French, the event $B$ - when decides to study German. What is the probability when a randomly picked student decides to learn both languages(Event $A\cap B$ ), if $P\left(A\right)=\frac{3}{4}, P\left(B\right)=\frac{2}{5}$ ?

Question 9:   There are $2$ red and $4$ blue balls in the box. Event $A$ happens when the first randomly picked ball is red. Event $B$ happens when second randomly picked ball is also red. Calculate $P_A\left(B\right)$ .

Question 10:   An archer hits the target with the probability $0.9$. What is the probability that out of three shots he hits the target only the third time?