In how many ways can 6 graduates line up to receive their diplomas if there are 4 girls and 2 boys and the girls will receive their diplomas

Ok

The girls have to come first in line.....Well, we have 4 ways to choose the first one, 3 ways to choose the second one, 2 ways to choose the third one and only 1 way to select  the fourth one.

So......4*3*2*1  = 4!  =  24 ways     (I think we talked a little bit about factorials earlier, didn't we??)

And, note that the boys come next...and we have 2 ways to choose the first one and 1 way to choose the second one.   So ...  2 * 1 = 2! = 2 ways

So....the total ways to line up the girls times the total ways to line up the boys is just.....24 * 2  = 48 ways

We can arrange the girls in 4! ways = 24 ways, and the boys in 2! ways = 2 ways.

So, 24 * 2 = 48 ways

CPhill , i dont understand anonymous's question neither ur answer ! pls can u explain it to me if u dont mind !

oh now i get it much nicely ! thank u very much for such a nice explanation !

i am happy becoz u explained me very nicely so this bouquet along with a thumbs up is from me to u !

Thanks for the flowers.....!!!!

ur welcome !

4P4*2P2=48

$${\left({\frac{{\mathtt{4}}{!}}{({\mathtt{4}}{\mathtt{\,-\,}}{\mathtt{4}}){!}}}\right)}{\mathtt{\,\times\,}}{\left({\frac{{\mathtt{2}}{!}}{({\mathtt{2}}{\mathtt{\,-\,}}{\mathtt{2}}){!}}}\right)} = {\mathtt{48}}$$

A different question:

6P2 means how many ways can 2 things be chosen from 6 where order counts.

There is a nPr button on your calculator Rosala.  See if you can find it and tell me what this answer is.

On the web2 calc it is nPr(6,2)=

melody when i clicked on the button and typed what u said the answer is coming 301 pls can u tell me what is going on in here (in ur answer )?

no 6P2=30

$${\left({\frac{{\mathtt{6}}{!}}{({\mathtt{6}}{\mathtt{\,-\,}}{\mathtt{2}}){!}}}\right)} = {\mathtt{30}}$$

My formula for the original question works out exactly the same as Chris's answer.

0! is defined as 1  SO my answer was really just 4!*2!=48 ways.

Try again to get the answer for 6P2 on your calculator.   

i thing i should just let this be becoz i havent studied these kind of things yet thats why im a bit unable to get u but still thumbs up from me for the answer !

Okay Rosala but i just wanted you to put 6P2 into your calculator and get 30.

But you are right you will not do this topic for a long time, so if you don't want to that is fine.  

Thank you for the thumbs up.   

ur welcome ! but i just wanted to tell that i got 30 when i entered nPr(6,2)=    !but i am unable to get on just typing 6P2 in the calculator !

On the web2 calc it is 

nPr(6,2)=

on your hand held calc it is probably 6  shift  nPr  2 =

nPr is usual the 2nd function one. the main thing on the top of the button is most likely nCr  can you find these symbols on your calculator rosala?

yes , i can find them !

okay so can you get the same calc answer as me?

 but i have answered u already , the answer is 30    !

6P2=30

Excellent Rosala.

That means that if 6 equally capable children run in a race and there is a distict 1st place and 2nd place (no ties)

then there are 30 different possibilities of who came 1st and 2nd.

thank u melody !