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# 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

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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 first?

Guest Jun 17, 2014

#3
+92367
+8

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

CPhill  Jun 17, 2014
#1
+92367
+5

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

So, 24 * 2 = 48 ways

CPhill  Jun 17, 2014
#2
+11852
0

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

rosala  Jun 17, 2014
#3
+92367
+8

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

CPhill  Jun 17, 2014
#4
+11852
+3

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 !

rosala  Jun 17, 2014
#5
+92367
0

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

CPhill  Jun 17, 2014
#6
+11852
0

ur welcome !

rosala  Jun 17, 2014
#7
+94085
+5

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  Jun 17, 2014
#8
+11852
0

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 )?

rosala  Jun 17, 2014
#9
+94085
+3

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.

Melody  Jun 17, 2014
#10
+11852
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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 !

rosala  Jun 17, 2014
#11
+94085
0

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.

Melody  Jun 17, 2014
#12
+11852
0

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 !

rosala  Jun 17, 2014
#13
+94085
+5

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?

Melody  Jun 17, 2014
#14
+11852
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yes , i can find them !

rosala  Jun 17, 2014
#15
+94085
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okay so can you get the same calc answer as me?

Melody  Jun 17, 2014
#16
+11852
+5

rosala  Jun 17, 2014
#17
+94085
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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.

Melody  Jun 17, 2014
#18
+11852
0

thank u melody !

rosala  Jun 17, 2014