Question

In how many ways can 5 boys and 5 girls be seated at a round table so that the boys and girls are seated alternately?

Answer 1

Answer choices are

14,400
2,880
576

Answer 2

@ShadowLegendX

Answer 3

Let's first put the boys in a circle.

Answer 4

How many ways can you arrange 5 boys in a circle ?

Answer 5

25

Answer 6

Nope, try again.

Answer 7

http://mathworld.wolfram.com/CircularPermutation.html

Answer 8

oops sorry how about 120

Answer 9

try again

Answer 10

um what do I multiply then?

Answer 11

it cant be 5 times 5

Answer 12

How good are you at permutations and combinations ?

Answer 13

eh

Answer 14

new to it

Answer 15

I know the whole

n
----r ! parts

Answer 16

Okay, good. Let me ask you a question.

Answer 17

and no I cant marry you sorry

Answer 18

that was a joke

Answer 19

Suppose you went to a restaurant and want to have breakfast with coffee.

There are 5 kinds of items to choose for breakfast,
and 4 kinds for coffee.

Answer 20

okay

Answer 21

Haha that's funny! So my question is how many different ways are there to have breakfast with coffee ?

Answer 22

the answer to that would be 5

Answer 23

oh sorry would it be 20

Answer 24

:P nope thats wrong too

Answer 25

120

Answer 26

5 ways to choose breakfast.

After you pick an item for breakfast, there are 4 choices for coffee.

Answer 27

Notice that for each type of breakfast, there are 4 choices for coffee.

Answer 28

naw so it would be 20

Answer 29

Yes! you see how it works right ?

Answer 30

Let's get back to our original problem

Answer 31

How to arrange 5 boys in a circle

Answer 32

Excellent! that is a nice way to visualize above problem

Answer 33

would it be 125 then?

Answer 34

Let's first arrange them in a straight line :

Answer 35

okay

Answer 36

For the first position, you can choose any one from the available 5 boys. So there are 5 ways for the first position :