An elementary school art class teacher plans to display artwork next to the door of each of the classrooms in the school. Each classroom door will only have one piece of artwork displayed, and the school has 22 such doors. If the teacher has 12 sketches and 16 oil paintings, what is the probability that 10 sketches and 12 oil paintings are chosen to be displayed?

Answer: Our required probability is 0.32.Step-by-step explanation:Since we have given that Number of doors to be selected in a manner  = 22Number of sketches = 12Number of oil paintings = 16Total number of doors we have =12+16 =28We need to find the probability that 10 sketches and 12 oil paintings are chosen to be displayed.So, probability would be [tex]\dfrac{^{12}C_{10}\times ^{16}C_{12}}{^{28}C_{22}}\\\\=\dfrac{66\times 1820}{376740}\\\\=\dfrac{120120}{376740}\\\\=0.3188\\\\\approx 0.32[/tex]Hence, our required probability is 0.32.