An algebra class has 6 students and 6 desks. For the sake of variety, students change the seating arrangement each day. How many days must pass before the class must repeat a seating arrangement? days must pass before a seating arrangement is repeated. Suppose the desks are arranged in rows of 3. How many seating arrangements are there that put Larry, Moe, & Curly in the front seats? There are seating arrangements that put them in the front seats.
+118723 An algebra class has 6 students and 6 desks. For the sake of variety, students change the seating arrangement each day. How many days must pass before the class must repeat a seating arrangement? days must pass before a seating arrangement is repeated.
This is the same as asking how many ways are there to arrange 6 people in a line.
Person one has 6 positions to choose from, person 2 has 5 positions to choose from and so on.
Total number of arrangements = 6! = 720
Suppose the desks are arranged in rows of 3. How many seating arrangements are there that put Larry, Moe, & Curly in the front seats? There are seating arrangements that put them in the front seats.
There are 3! =6 ways of seating Larry, moe and curly in the front seats
and
there it 3!=6 ways of seating the other 3 in the back seats.
so altogether there are 6*6=36 arrangements were L,M and C are in the front seats.
