Question

in how many orders can 5 girls and 3 boys walk through a doorway when order does matter? when order doesn't matter?

Answer 1

if order does does matter, then by the counting principle there are
\[8
!=8\times 7\times 6\times 5\times 4\times 3\times 2\] ways

Answer 2

the wording of the question doesn't make any sense really
"n how many ORDERS can 5 girls and 3 boys walk through a doorway when ORDER does matter?"

Answer 3

the second part really makes no sense
what does "how many ways can 8 people walk through a door when order doesn't matter? "
what on earth is that supposed to mean?
i guess the answer is one, they all walk through together

Answer 4

How many orders can they walk in if there are restrictions? How many orders can they walk in without restrictions? ....sorry

Answer 5

what restrictions?

Answer 6

girls walk through before boys

Answer 7

either i am missing something or the question is illiterate

Answer 8

I didn't read thoroughly enough as I typed. How many ways can the kids walk through the doorway if there are no rules/restrictions as far as who goes when? How many ways can the kids walk through if the girls must walk through before the boys

Answer 9

if there are no restrictions then the answer is the one i wrote above
8 choices for the first persone
7 for the second
6 for the third
5 for the fourth
4 for the fifth
3 for the sixth
2 for the seventh
1 for the eighth
by the counting principle the total number of ways to do this is \[8!=8\times 7\times 6\times 5\times 4\times 3\times 2\]
i.e. you multiply the number of ways

Answer 10

second one is similar, but since girls go before boys and there are 5 girls and 3 boys it is
\[5!\times 3!\]

Answer 11

thank you!