Question

in how many ways can six people be lined up for a photograph of ralph must stand immediately to the left of bernice

Answer 1

Hint:

If ralph must stand immediately to the left of bernice, then the grouping of ralph and bernice forms one "person" so to speak. This is because ralph must always be to the left of bernice and you can think of these two slots as one big slot

so you really have 6-1 = 5 people total and you're ordering them 5 different ways

Answer 2

yes

Answer 3

does that make sense?

Answer 4

wait there's more. can u contitnue?>

Answer 5

how many ways are there to order 5 people?

Answer 6

5*4*3*2*1 ok thanks haha

Answer 7

yep 120 ways

Answer 8

hey what about this one? in how many ways can nine people be lined up for a photograph if clark and billy must not stand next to each other

Answer 9

Let's count how many ways clark and billy can stand next to each other

So there are 2*8! = 80640 ways for them to do this

Answer 10

There are 9! = 362880 different ways to order 9 people

So there are 9! - 2*8! = 362880 - 80640 = 282240 ways for them to line up where clark and billy must not stand next to each other

Answer 11

wait so why is it not just 2*8! ?

Answer 12

because 2*8! is the number of ways to order them where clark and billy are next to each other

Answer 13

basically you combine clark and billy into one person to go from 9 people to 8 people

Answer 14

oh I c... so 2*8! is just the way them two can order. but u subtract to also include the other members. ok tahnks!!!

Answer 15

yep, yw

Answer 16

oh wait so can u tell me how u know to times 2?