SOLUTION: How many different committees of three members can be formed from a group of eight people?

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Question 76801: How many different committees of three members can be formed from a group of eight people?
Found 2 solutions by Edwin McCravy, Cintchr:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Two students at Sky High School will be chosen for a TV interview. If there are
900 students at school, how many different selections are possible?
                 
C(900,2) = (900·899)/(2·1) = 404550

Twenty people report for jury duty. How many different 12-person juries can be
chosen?

C(20,12) = (20·19·18·17·16·15·14·13·12·11·10·9)/(12·11·10·9·8·7·6·5·4·3·2·1)
= 125970

How many different committees of three members can be formed from a group of
eight people?
	
C(8,3) = (8·7·6)/(3·2·1) = 56
	
Edwin

Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
Label the eight people as A B C D E F G H
Now list the combos that can be made

The A list
ABC ABD ABE ABF ABG ABH
ACD ACE ACF ACG ACH
ADE ADF ADG ADH
AEF AEG AEH
AFG AFH
AGH
21

The B list
BCD BCE BCF BCG BCH
BDE BDF BDG BDH
BEF BEG BEH
BFG BFH
BGH
15

The C list
CDE CDF CDG CDH
CEF CEG CEH
CFG CFH
CGH
10

The D list
DEF DEG DEH
DFG DFH
DGH
6

The E list
EFG EFH
EGH
3

The F list
FGH
1

Add up all the combos
21 + 15 + 10 + 6 + 3 + 1 = 56