Ten students need to present their reports. Five can present each day. How many ways can the teacher choose a group of five students to present their reports on the first day? How many ways can the teacher choose a group of 5 students to present on the first day if Marjorie must present on the first day?

Solution:There are a total of 10 student.when Teacher is supposed to choose 5 Students randomly from the group of 10.The selection can be done in[tex] =10_C_{5} \ \ ways [/tex][tex] \\\\=10_C_{5}=\frac{10!}{5!5!} \\\\=252 \ \ ways. [/tex]when Teacher is supposed to choose 5 Students randomly from the group of 10, if Marjorie must present on the first day.The number of ways[tex] 9_C_{4}=\frac{9!}{4!5!}=126 [/tex]