IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: astarmathsandphysics on October 11, 2009, 12:13:20 pm

Title: Combinatorics
Post by: astarmathsandphysics on October 11, 2009, 12:13:20 pm

a box contains sweets of 6 different flavours. There are at least 2 sweets of each flavour. A girl selects 3 sweets from the box. Given that these 3 sweet are not all of the same flavouor, calculate the no. of different ways she can select her 3 sweets.

6C3 ways of secting 3 sweets altogether but 6 of these have all same colour so ans=6C3-6
Title: Re: Combinatorics
Post by: slvri on October 11, 2009, 03:45:01 pm
a box contains sweets of 6 different flavours. There are at least 2 sweets of each flavour. A girl selects 3 sweets from the box. Given that these 3 sweet are not all of the same flavouor, calculate the no. of different ways she can select her 3 sweets.

6C3 ways of secting 3 sweets altogether but 6 of these have all same colour so ans=6C3-6

the answer should be 50
Title: Re: Combinatorics
Post by: astarmathsandphysics on October 11, 2009, 04:04:09 pm
6*5*4/6 =20 no two the same colour
6*5*2/3=20 two the same colour
40 ways altogether
 
Title: Re: Combinatorics
Post by: slvri on October 11, 2009, 04:53:16 pm
6*5*4/6 =20 no two the same colour
6*5*2/3=20 two the same colour
40 ways altogether
 
6C3=20 no two of the same colour
6*5=30 two of the same colour
total=30+20=50
when i gave my teacher this q he couldnt solve it
Title: Re: Combinatorics
Post by: astarmathsandphysics on October 12, 2009, 11:45:11 am
my reasong for 6*5*2/3 is this: For the first you have a choice of 6 and for the second a choice of 5. For the tird you can have the first or second colour, hence the factor of 2 and divide by three because the odd colour can be 1st, 2nd, or third.
Title: Re: Combinatorics
Post by: slvri on October 12, 2009, 12:41:29 pm
my reasong for 6*5*2/3 is this: For the first you have a choice of 6 and for the second a choice of 5. For the tird you can have the first or second colour, hence the factor of 2 and divide by three because the odd colour can be 1st, 2nd, or third.
but couldnt the logic also be this: for the first and second sweets you have a choice of 6 and for the third sweets you have a choice of 5 so 6*5=30
im confused...... ???
Title: Re: Combinatorics
Post by: astarmathsandphysics on October 12, 2009, 01:02:15 pm
The sweets can be picked in any order and the order doesnt matter. Things get much worse because you can have two sweets the same colour but not three.