Perms and combs questions (1 Viewer)

[Evergreen]

I have worked out answers to these but not sure if they are right

a. A class debating group consists of 12 students, 8 of whom are girls. How many debating teams of 4 can be formed allowing:

i. no girls at all

ii. exactly 1 girl

iii. at least 1 girl

iv. equal number of boys and girls

v. if 1 particular girl, mary, is to be excluded, but one particular boy, john, is to be included.

b. the letters of the word GEOMETRY are arranged in a straight line. How many arragnements are possible:

i. if the vowels must occupy the 2nd, 4th and 6th places.

ii. if the arragnement is to begin and end with the letter E.

iii. if the 2 Es are to be seperated.


My answers:
ai. 1
ii. 32
iii. 494
iv. 168
v. 120

bi. 720
ii. 1440
iii. 10080

 

[pLuvia]

I'm going to assume that allowing "exactly how many girls/boys" as in the number of girls/boys is included in the sample where you are choosing from

Think about these answers again

ii)
iv)
b)i)
ii)
iii)

 

[Evergreen]

bi.

GEOMETRY

umm total no. of ways it can be arranged is 20160. 3!/2! ways for vowels to occupy 2nd, 4th and 6th. so total no. is 20160- 3!/2!= 20157? wait that doesnt look right...

or i did it another way. 3!/2! x 5!= 360?

ii. lol i forgot you cant swap Es around so that would be 720 right?

iii. the method i use for this type is to eliminate any possibility of the Es being next to eachother. so that would be 1!x7. answer is 8!/2! - 1!x7= 20153?

 

[Kujah]

ii)
iv)

?

i. exactly 1 girl? Wouldn't it just be 8C3 x 4C1
iv. equal numbers. 8C2 x 4C2

 

[Evergreen]

ii)
iv)

?

i. exactly 1 girl? Wouldn't it just be 8C3 x 4C1
iv. equal numbers. 8C2 x 4C2

8 are girls and therefore 4 are boys.

and yeh i got your answer for iv too.

 

[achidiac]

P&C are so hard -.-

 

[iEdd]

So did you get all of them?

I'll have a crack at any you haven't gotten (I need the revision too!).

P&Cs are fun.

 

[random1990]

ok these are the answers i get (just ask if u need explaining):
ai. 1
aii. 32
aiii. 494
aiv. 168
av. 120

bi. 360
bii. 720
biii. 15120

 

[Hikari Clover]

回复: Re: Perms and combs questions

my answer, same as random1990's......