@jim_thompson5910

how many committees of four can be chosen from twelve students?

how many of these will include a given student?

how many will exclude a given student?

Question

@jim_thompson5910 

how many committees of four can be chosen from twelve students? 

how many of these will include a given student? 

how many will exclude a given student?

jim_thompson5910 · Answer

how many committees of four can be chosen from twelve students?

use n C r = (n!)/(r!*(n-r)!)

where n = 12 and r = 4

anonymous · Answer

yes i get the first question. but what about hte second and third?

jim_thompson5910 · Answer

well if a student must be on the committee, then you have 4-1 = 3 slots left

and you have 12-1 = 11 people to fill those 3 slots

jim_thompson5910 · Answer

does that help?

anonymous · Answer

how did u know that?

jim_thompson5910 · Answer

you have 4 slots to start with

jim_thompson5910 · Answer

a certain student (say student X) must be on this committee

jim_thompson5910 · Answer

So you go from

_ _ _ _

to

X _ _ _

jim_thompson5910 · Answer

that's why you have 3 slots left and 11 people left to fill them

anonymous · Answer

ok so that's the second question then what's third quesiton

jim_thompson5910 · Answer

parts b and c are the complete opposite

jim_thompson5910 · Answer

if you know how many ways to order a committee with student X on the committee, then you can find out how many ways to have student X off of the committee

kropot72 · Answer

If one student is excluded there are only 11 to choose from. 11C4

anonymous · Answer

the answer to these questions were 495, 165, 330

jim_thompson5910 · Answer

a) 12 C 4 = 495

b) 11 C 3 = 165

c) 11 C 4 = 330 (notice how 11 C 3 + 11 C 4 = 12 C 4)

so that's how they got those answers

anonymous · Answer

i get the first two questions rihgt... but number three im still confused

jim_thompson5910 · Answer

basically the numbers from parts b and c must add up to the total of 495

jim_thompson5910 · Answer

so that's why 165 + 330 = 495

kropot72 · Answer

Do you know how to calculate 11C4 ? This gives the answer to number 3 question.

anonymous · Answer

yes i do. but getting 11C4 im stil thinking about it

anonymous · Answer

like why not 12c4? like how u guys know its 11?

jim_thompson5910 · Answer

because you can't pick the student X if you're keeping him/her off the committee

jim_thompson5910 · Answer

you have 12-1 = 11 choices left

but you still have 4 slots

anonymous · Answer

haha alrhgt thank you i get it now!

jim_thompson5910 · Answer

ok that's great

anonymous · Answer

lol omg haha lol ofcourse its 11 cuz u kick him off tahnks dude!

jim_thompson5910 · Answer

yw