[~*Amethyst*~]

Can anyone help in how to work out a 'Family Maths Question' please.

Family Maths Challenge 2

At your party you have decided to serve triple decker ice creams!
* There are 5 yummy flavours - peppermint, chocolate, strawberry, banana and tutti frutti.
* How many combinations of three flavours could you create?
* How many combinations of three flavours could you create if one flavour is always chocolate?
* How many combinations all together (including 3 scoops the same, 2 the same and one different)?

XxxAmethyst

[secret~sammy]

1) 5 chose 3 = 10

nCr = n! / (n - r)! r!

nCr = 5!/ (5 - 3)! 3!
nCr = 5!/ 2! 3!
nCr = (5 * 4 * 3 * 2 *1) / (2 * 1)(3 * 2 * 1)
nCr = 120 / (2 * 6)
nCr = 120 / 12
nCr = 10

2) 4 choose 2 (because 1 is always choc) = 6 by the formula above

3) 5^3 = 125

[Georgie01]

How many combinations of three flavours could you create?

5x4x3=60 (you have 5 choices for the first flavour, then 4 for the second, 3 for the third since you aren't allowed to repeat any flavours)

* How many combinations of three flavours could you create if one flavour is always chocolate?

1x4x3=12 (1 choice is chocolate then 4 (all except chocolate) then 3 (not chocolate and not the second flavour)

How many combinations all together (including 3 scoops the same, 2 the same and one different)?

5x5x5=125 (because you can choose any of the five flavours for each scoop)

(hoping that I haven't done something wrong, seems to make sense )

[CrazySingleMum]

OMG I can't understand that formula ... it's not really a Year 4 question???
ETA: Georgie01, that answer makes more sense to me, still seems difficult for the age, but that could be because of my lack of maths skills.

This post has been edited by CrazySingleMum: 11/02/2013, 06:52 PM

[Peppery]

1. 15

2. 6

3. 125

Honestly these are guesses, my father was a mathematician (retired) would be absolutely horrified at my lack of mathematical reasoning

[AvadaKedavra]

Georgie's answer is correct.

I remember doing combinations in primary school.

[libbylu]

Does the order of the flavours matter? If not, then the first poster is correct, if not, then the second poster is correct!
Does seem very complex for year 4.

[jayskette]

1) 5*4*3
2) 4*3*2 - edited to say - oops... should be 4*3
3) 5*5*5

This is actually an extension maths question... unless the grade 4 people are smarter than when I did this as an extension when I was in year 4... lol

Try this one (another "extension" question on ratios that I actually got in year 4)

There is a piece of orchestral music that is played by 60 Strings, 60 Woodwind and 40 Brass, and it lasts 2 minutes 35 seconds.
How long will the music take to be played if it is played by 40 Strings, 30 Woodwind and 20 Brass?

ROFL

This post has been edited by jayskette: 11/02/2013, 07:03 PM

[Georgie01]

My grade 4 has done a little bit of this sort of thing - I work through it with him the way that I did here. It can help to use a diagram or find five different things an do a bit of a model to understand the reasoning.

I haven't had to use factorials with him as the worksheets ask him to explain how he thought things through and I'm fairly sure he hasn't learned factorials/combinations/permutations formally.

Does the order of the flavours matter? If not, then the first poster is correct, if not, then the second poster is correct!

Ahhh, thank you! I need to brush up.

Yes, my answers assume that choc/strawberry/banana is different to choc/banana/strawberry, Secret~Sammy's solution calls those the same...

Reading the question again Secret Sammy is right because the question asks for combinations so it's implied that the order doesn't matter and choc/strawberry/banana=strawberry/banana/choc etc. Not sure how I'd help a year 4 work through that logically other than with a chart (assuming they haven't actually been taught the formula)


This post has been edited by Georgie01: 11/02/2013, 07:23 PM

[amabanana]

There is a piece of orchestral music that is played by 60 Strings, 60 Woodwind and 40 Brass, and it lasts 2 minutes 35 seconds.
How long will the music take to be played if it is played by 40 Strings, 30 Woodwind and 20 Brass?

This post has been edited by amabanana: 11/02/2013, 07:07 PM