Eli has 7 black pens and 5 blue pens in his desk drawer. He also has 3 yellow highlighters, 2 green highlighters, and 5 pink highlighters in his pencil case. If he chooses one pen and one highlighter without looking, what is the probability that he will get a black pen and he will not get a green highlighter?
First, let's calculate the total number of choices Eli could make:
Total number of pens = 7 black pens + 5 blue pens = 12 pens
Total number of highlighters = 3 yellow highlighters + 2 green highlighters + 5 pink highlighters = 10 highlighters
Total number of choices = 12 pens * 10 highlighters = 120 choices
Now, let's calculate the number of favorable outcomes where Eli gets a black pen and does not get a green highlighter:
Number of black pens = 7
Number of non-green highlighters = Total number of highlighters - Number of green highlighters = 10 - 2 = 8
Number of favorable outcomes = Number of black pens * Number of non-green highlighters = 7 black pens * 8 non-green highlighters = 56 outcomes
Finally, let's calculate the probability:
Probability = Number of favorable outcomes / Total number of choices
Probability = 56 / 120
Probability = 7 / 15
Therefore, the probability that Eli will get a black pen and will not get a green highlighter is 7/15.