Question

Can someone please help me with Permutation? :)
3 boys and girls are to be photographed. In how many ways can they be arranged in a row:
(a) if the girls are photographed by themselves.
(b) if the boys are photographed by themselves.

Answer 1

ok, so let the boys be ABC and the girls be DEF if u are just looking at the girls, you can do DEF EFD DFE FED FDE EDF, so 6 different ways, and since there are the same amount of boys, it would be the same just different letters

Answer 2

ohhh.. so the answer is 12??

Answer 3

o, theres only 2 girls...

Answer 4

and im assigned to answer no. 8 can you help me with the rest. if its ok with you?

Answer 5

O.O i would have to work on that at home, im in school right now >_< someone can probrably answer it for u before then

Answer 6

which one you need help with?

Answer 7

well its ok.. thanks Dragonborn :)

Answer 8

i need help answering a - g can you help me? please

Answer 9

sure lets do the easy one first
two girls, a and b
ab, ba
two ways to do it

Answer 10

3 boys, x, y, z
xyz
xzy
yxz
yzx
zxy
zyx

six ways to do it

Answer 11

now you don't want to continue to have to write all the combinations, so we think
3 boys
3 choices for first one
2 for the second
1 for the third
by the counting principle the number of ways to do this is
\[3\times 2\times 1\] often written as \(3!\)

Answer 12

ohhhh.. haha i think i kinda get it.

Answer 13

that makes the next one easy
5 people arranged in a row, number of ways to do it is
\[5!=5\times 4\times 3\times 2\times 1\]

Answer 14

now we get to a harder one
boy, girl, boy, girl, boy

but it is not that hard
3 choices for the first boy
2 choices for the first girl
2 choices for the second boy
1 choice for the second girl
1 choice for the last boh

by the counting principle, the number of ways to do this is
\[3\times 2\times 2\times 1\times 1\]

Answer 15

notice that we did not use any formula at all, it was all based on the counting principle, and reasoning how many choices at each step
all the formulas are based on that as well

Answer 16

ohhhh....

Answer 17

soo letter g is the answer 24?? im not that sure though

Answer 18

the row begins and ends with a girl?

Answer 19

how many choices for the first girl ?

Answer 20

3 choices for the first boy
2 choices for the first girl
2 choices for the last boy
ohh imeant 12 and letter e ! .. hahahhaa sorry

Answer 21

i dunno if its right

Answer 22

ok now i have to go back and look
why don't you do g whilst i check your e ?

Answer 23

ok :)

Answer 24

you are close withe, but it not quite right, we can fix it though
let me know what you get for f, take a look at the diagram i sent

Answer 25

2 x 3 x 2 x 1 x 1 = 12 also ??

Answer 26

yes, that is right

Answer 27

that is for f,

Answer 28

Hi!...I don't mean to interrupt but if you watch this video, I think you might just master permutations! :o)
https://www.youtube.com/watch?v=XqQTXW7XfYA

Answer 29

good work!
now we have to redo e more carefully, because it is not 12

Answer 30

(f) if no boy sits next to a girl.

Answer 31

ill try watching it :)) thankyouu @SinginDaCalc2Blues

Answer 32

oh i got confused, the answer of 12 is for question g not f
want to do f next ?

Answer 33

yeah. hahaha

Answer 34

but honestly i dont know how to do F

Answer 35

i'm all messed up with the letters, so lets just say what the question is

Answer 36

ok.. hahhaha :D

Answer 37

how can they be arranged if no boy sits next to a girl?

Answer 38

i would say that was impossible in one row

Answer 39

I Know Right!! like honestly i dont get it

Answer 40

what is wrong with saying 0 ways?

Answer 41

hahhahaha.. i think its valid.. sooo 0 ways then

Answer 42

some boy has to sit next to some girl for sure, so zero is a perfectly good answer

Answer 43

which ones are left?

Answer 44

uhhmm.. is my e alright?? the question is "if the row begins and ends with a boy?"

Answer 45

3 x 1 x 2 x 1 x 2 = 12 ways ???

Answer 46

B ? ? ? B

Answer 47

3 for the first by
2 for the last so you had that part correct

Answer 48

but the middle should be \(3\times 2\times 1\) because you have 3 people to choose from

Answer 49

\[3\times 3\times 2\times 1\times 2\]

Answer 50

im incorrect.. how come 3 x 2 x 1??

Answer 51

sorry i kinda dont get it. hahahahahaha

Answer 52

you have 3 choices for the first by right? and 2 choices for the last boy
you said that and got that part right

Answer 53

now that leaves 3 people, (2 girls and a boy) but it doesn't matter what gender they are, they can sit in the middle 3 spots in any order at all

Answer 54

and the number of ways you can seat three people in three chairs is \(3!\)

Answer 55

ooohh :D soo the answer is 36 ways

Answer 56

yes, i think so
now what is left ?

Answer 57

i think were all done!!!

Answer 58

THANKYOOUUU SOO MUCH @satellite73

Answer 59

yw
hope you learned how to do more if you need to