MathDB

17

Part of 2019 AMC 10

Problems(2)

He stacc Bloccs

Source: 2019 AMC 10A #17

2/8/2019
A child builds towers using identically shaped cubes of different color. How many different towers with a height 88 cubes can the child build with 22 red cubes, 33 blue cubes, and 44 green cubes? (One cube will be left out.)
<spanclass=′latex−bold′>(A)</span>24<spanclass=′latex−bold′>(B)</span>288<spanclass=′latex−bold′>(C)</span>312<spanclass=′latex−bold′>(D)</span>1,260<spanclass=′latex−bold′>(E)</span>40,320<span class='latex-bold'>(A) </span> 24 \qquad<span class='latex-bold'>(B) </span> 288 \qquad<span class='latex-bold'>(C) </span> 312 \qquad<span class='latex-bold'>(D) </span> 1,260 \qquad<span class='latex-bold'>(E) </span> 40,320
AMCAMC 10AMC 10 A2019 AMC 10A2019 AMCcounting
Red Ball is Superior

Source: 2019 AMC 12B #13 / AMC 10B #17

2/14/2019
A red ball and a green ball are randomly and independently tossed into bins numbered with positive integers so that for each ball, the probability that it is tossed into bin kk is 2−k2^{-k} for k=1,2,3,….k=1,2,3,\ldots. What is the probability that the red ball is tossed into a higher-numbered bin than the green ball?
<spanclass=′latex−bold′>(A)</span>14<spanclass=′latex−bold′>(B)</span>27<spanclass=′latex−bold′>(C)</span>13<spanclass=′latex−bold′>(D)</span>38<spanclass=′latex−bold′>(E)</span>37<span class='latex-bold'>(A) </span> \frac{1}{4} \qquad<span class='latex-bold'>(B) </span> \frac{2}{7} \qquad<span class='latex-bold'>(C) </span> \frac{1}{3} \qquad<span class='latex-bold'>(D) </span> \frac{3}{8} \qquad<span class='latex-bold'>(E) </span> \frac{3}{7}
2019 AMC 12BAMCAMC 12AMC 12 Bprobability2019 AMC2019 AMC 10B