Math Is Fun Forum

sydneydad

Member

Registered: 2014-03-16

Posts: 9

Question

Hi all,

Got the following question for my son's homework and I think the way to solve this is as follows:

5 diff colour
3 available spots
any combination of 3 colours is considered as 1 flag

so 5x5x5 = 125

am I correct ?

Thanks

Last edited by sydneydad (2014-03-20 14:18:15)

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Question

Is the same colour allowed in adjacent bands? If so, then it's 125. If not, then it's 5*4*4. If no colour can be repeated at all, then it's 5*4*3.

sydneydad

Member

Registered: 2014-03-16

Posts: 9

Re: Question

Is the same colour allowed in adjacent bands? If so, then it's 125. If not, then it's 5*4*4. If no colour can be repeated at all, then it's 5*4*3.

The question says

"The flag must have 3 bands of colour, but the colours can be in any order. How many different flags can the class design ?"...this is what I'm confused about the question do we assume that we can treat each combination of 3 colours as 1 flag or we are only allowed to user 1 combination of flag ?

sydneydad

Member

Registered: 2014-03-16

Posts: 9

Re: Question

Is the same colour allowed in adjacent bands? If so, then it's 125. If not, then it's 5*4*4. If no colour can be repeated at all, then it's 5*4*3.

ShivamS,

Can you tell me more how the 5*4*4 and 5*4*3 play out ?

eigenguy

Member

Registered: 2014-03-18

Posts: 78

Re: Question

Duplicate colors allowed, but not adjacent:

The middle band can have 1 of 5 colors. The top band can be any color except the one chosen for the middle, so 4 colors. The bottom band can have any color except the one chosen for the middle, so 4 colors again. That makes 5 * 4 * 4 combinations.

The calculation for no two colors the same is almost identical, but then the bottom band can't have the same color as either the middle or the top band, so 5 *4 * 3.

---

"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

sydneydad

Member

Registered: 2014-03-16

Posts: 9

Re: Question

Duplicate colors allowed, but not adjacent:

The middle band can have 1 of 5 colors. The top band can be any color except the one chosen for the middle, so 4 colors. The bottom band can have any color except the one chosen for the middle, so 4 colors again. That makes 5 * 4 * 4 combinations.

The calculation for no two colors the same is almost identical, but then the bottom band can't have the same color as either the middle or the top band, so 5 *4 * 3.

Thanks eigenguy..that make sense for me now.