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anonymous
 one year ago
MEDAL!!
(suppose there is a group of 7 people from which we will make a committee)
In how many ways can we pick a threeperson committee?
anonymous
 one year ago
MEDAL!! (suppose there is a group of 7 people from which we will make a committee) In how many ways can we pick a threeperson committee?

This Question is Closed

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2Let's say we have 3 slots A,B,C how many do we have to choose from for slot A?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0Correct, then for slot B?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0Recall that one of the sever is already in slot A.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yep, and then C?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yes, you'll multiply 7, 6 and 5

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2that won't be your final answer but it gets you closer

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2210 is the number of ways to pick 3 people IF order mattered but there is no ranking on this committee, so order doesn't matter

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2so what you have to do is divide by 3! = 3*2*1 = 6 to get the correct count

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2the reason why is because there are 6 ways to order any three objects xyz xzy yxz yzx zxy zyx

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2210/6 actually

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ah okay. I read your response wrong haha so 35

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2another way is to use the combination formula \[\Large _n C _r = \frac{n!}{r!*(nr)!}\] with n = 7 and r = 3 and you'll get the same answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 what if it was a fourperson committee instead? wouldn't it be 7C4=35? also?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2that is correct

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2if you think of it in terms of 7 slots A through G we have this dw:1441932178631:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2now imagine cutting a line through that group such that one side (say the left side) has 3 slots and the other side has 4 slots dw:1441932241059:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2arranging 7 people to go in slots A through C is the exact same as arranging the remaining 4 to go in D through G so that's why 7 C 3 = 7 C 4 in general \[\LARGE _n C _x = \ _n C _y\] where x+y = n (so in this case, x+y = 3+4 = 7 which is the value of n)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, that is the way my instructor explains it also, thanks again!

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you're welcome
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