1. A Premier has six members of his caucus who are interested in joining a special committee. The committee is to consist of the premier himself and three other MLA's. The premier is considering how to create the committee to appear demographically diverse. The candidates are as follows: - Alice is a 42-year-old woman from Saskatoon who is of mixed English-Irish background. - Byron is a 25-year-old man from Regina. His parents immigrated from Trinidad. He is of mixed African-European-Indian race but self-identies as \black". - Ciaran is a 60-year-old farmer from the Cypress Hills area. In spite of his Celtic name, he is the descendant of Norwegian settlers. - Darlene is a 30-year old Dene woman from the Fond-du-Lac First Nation. - Edward is a 33-year-old doctor working in Lipton. He is third-generation Chinese. - Fiona is a 49-year-old Cree woman living in Prince Albert. The Premier himself is from Saskatoon, 50 year old, and is of German origin. (Any resemblance to actual MLA's, past, present, or future, is entirely coincidental.) (a) List all the possible committees that could be constituted from these people. (You may use just the initial letter of each name, for brevity. Use \P" for the Premier.) Consider this list as a sample space. (b) Display the event that the committee is gender-balanced, by listing its atoms, (i.e. list all the possible committees that have an equal number of men and women). (c) Similarly, display the event that the committee includes at least one indigenous person, (d) the event that the committee includes (at least) one indigenous person and one visible minority person, (e) the event that the committee has equal representation from urban and rural communities, (f) the event that the committee includes both a woman and a visible minority, and (g) the event that the committee includes a visible minority woman.