Question

There are 11 students in a very small 3rd grade class. In how many ways can the 11 students be lined up to go out for recess? The teacher needs to choose two students to serve on the 3rd grade council. In how many ways can she do that? The teacher needs to select a hall monitor, a board cleaner, and a lunch hauler for the class. In how many ways can she assign students to these three positions?

Answer 1

1)as order does not matter for serve in  3rd grade council being both posiition of same rank hence we will use combination

number of ways to select 2 students to serve on the 3rd grade council =¹¹C₂=11!/(2!*(11-2)!)=55

2)

as to assign students to   hall monitor, a board cleaner, and a lunch hauler involve different ranks hence we need to arrange then in order therefore we will use permutation

ways shecan assign students to these three positions=¹¹P₃ =11!/(11-3)!=990