The students in group 1 earned 10 extra minutes of recess by winning a class competition. before going out for their extra recess time, they form a single file line. in how many ways can they line up?

Full Question:

Mrs. Steffen's third grade class has 30 students in it. The students are divided into three groups (numbered 1, 2, and 3), each having 10 students. (a) The students in group 1 earned 10 extra minutes of recess by winning a class competition. Before going out for their extra recess time, they form a single file line. In how many ways can they line up? (b) When all 30 students come in from recess together, they again form a single file line. However, this time the students are arranged so that the first student is from group 1, the second from group 2, the third from group 3, and from there on, the students continue to alternate by group in this order. In how many ways can they line up to come in from recess?

1. 3628800 ways

2. 10886400

Step-by-step explanation:

A.

If group 1 students earn 10 extra minute for recess.

A student in group 1 have 1 of 10 positions to fill in

Another student has 9 possible positions

Another has 8 possible positions

Till it gets to the last

So, The 10 students have 10! Number of ways to line up

10! = 3628800

B.

Each of the group have 30 positions to line up

But they must be lined up in 3s (to accommodate each group)

Group 1 has 10! Ways of lining up;

Group 2 has 10! Ways

Group 3 has 10! Ways

So, possible arrangements = 10! * 3

= 10886400

120 seems like the most sensible answer.

step-by-step explanation:

if there is only one topping on all caramel apples and there's 120 of them. then all apples should/will be covered in sprinkles. make sense?