Problems(2)
Consider the numbers 1 through 6 numbered on the coins below. Ella takes a coin from each of the three columns. Bella takes a coin from each of the remaining two columns. Cassandra takes the remaining coin. In how many ways could they have taken out the six coins? [asy]
size(100);
draw(Circle((0,0),0.45));
label("1",(0,0));
draw(Circle((0,1),0.45));
label("2",(0,1));
draw(Circle((0,2),0.45));
label("3",(0,2));
draw(Circle((1,0),0.45));
label("5",(1,0));
draw(Circle((1,1),0.45));
label("4",(1,1));
draw(Circle((2,0),0.45));
label("6",(2,0));
[/asy]
<spanclass=′latex−bold′>(A)</span>9<spanclass=′latex−bold′>(B)</span>12<spanclass=′latex−bold′>(C)</span>15<spanclass=′latex−bold′>(D)</span>18<spanclass=′latex−bold′>(E)</span>20 2022 A Individual
Sarah is leading a class of 35 students. Initially, all students are standing. Each time Sarah waves her hands, a prime number of standing students sit down. If no one is left standing after Sarah waves her hands 3 times, what is the greatest possible number of students that could have been standing before her third wave?
<spanclass=′latex−bold′>(A)</span>23<spanclass=′latex−bold′>(B)</span>27<spanclass=′latex−bold′>(C)</span>29<spanclass=′latex−bold′>(D)</span>31<spanclass=′latex−bold′>(E)</span>33 2022 B Individual