Math Is Fun Forum

chetah

Member

Registered: 2008-02-15

Posts: 32

Combinations

A certain ice cream store has 31 flavours of ice cream available.  In how many ways can we order a dozen icreams cones if
(a) we do not want the same flavour more than once?
(b) a flavour may be orders as many as 12 times?
(c) a flavour may be ordered no more than 11 times?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Combinations

31 flavours:
a,b,c,d,e,f,...x,y,z is 26 plus 5 more named: #, $, %, &, and *.

for (a), if you order these 12:  yesiwantcold, then is dloctnawisey the same thing?

So like is backwards the same thing, that's what I want to know?

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igloo myrtilles fourmis

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: Combinations

(a)   Choosing 12 from 31 ,  31!/(12!x(31-12)!) =141120525
(b)    31^12
(c)   If each one could be ordered 12 times, then 31^12,  If could only be ordered 11 times, then there are 31 situations, which each flavor is ordered 12 times,  so  its will be 31^12 -31

hope I get it right XD