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Finding all possibilities problems.

Just having a go at some of these “finding all possibilities” problems and think I am on the correct path, just wanted to get some other peoples’ thoughts on them-especially any of you who are super at maths!

1) A restaurant has 4 starters, 4 mains and 4 desserts. How many different combinations of starters, main courses and desserts can be had?

2) There are 5 different coloured cars – red, blue, white, green and black

There are 5 different coloured wheels – red, blue, white, green and black.

There are 5 different coloured spoilers – red, blue, white, green and black.

There are 5 different coloured exhaust tips – red, blue, white, green and black.

The problem is. How many different combinations of car colours, wheels, spoilers and exhaust tips are there?
A car must have all accessories fitted i.e. must have wheels, spoiler and an exhaust

So one example 1 – could have:
Red car-red-wheels-red spoiler-red exhaust
Example 2
Red car-red wheels – red spoiler – blue exhaust

I do have some ideas of formulas to work these out rather than trying to go through all possibilities by hand but I am struggling to know if they are correct. I won’t put my ideas down so you can have a fresh start too!

Many thanks

would it not be 4x4x4 and 5x5x5x5

or am I just the stupid one

That is my initial thoughts but didn't know if it would be 4 x 3x2 or 5x4x3x2

wrekka wrote:That is my initial thoughts but didn't know if it would be 4 x 3x2 or 5x4x3x2

Incorrect, you'd decline numerically as the formula plays out ;
Ie, Option 'A + B' in the first equation wouldn't obviously be the same as option 'B+A'
Therefore if you were to list them logically in something like in excel with cars being A and wheels being B etc, and then for colours - red being 1, blue 2 etc, then you'd get as follows ;

A1B1C1D1E1
A1B1C1D1E2
A1B1C1D1E3
...
...
...
...
E5E5E5E2
E5E5E5E3
E5E5E5E4
E5E5E5E5

This would show that A has 5x5x5x5x5, B has 5x5x5x5x5 etc etc
You could then apply this same formula to any different combinations
Hope this helps and that I'm correct as I'm two glasses of wine in and it's been a long day haha ?

Pie wrote:http://www.prepfortests.com/gmat/tutorials/permutations

An interesting site
cheers

wrekka wrote:

Pie wrote:http://www.prepfortests.com/gmat/tutorials/permutations

An interesting site
cheers

'Interesting' is a word I'd really only use very loosely for mathematical equations, especially in public ! haha

From memory the answer to the firs one is either 4 to the power of 3 or 3 to the power of 4, can't remember which way round it is. The 2nd one is more obvious as 5 to the power of 5.
It's been a long time though!

4 to the power 3 and 5 to the power 4

P_G wrote:4 to the power 3 and 5 to the power 4

Thanks for all the responses a couple threw me a little

so to confirm:

Problem 1 is 4 to the power of 3 = 4 x 4 x4 = 64 meal combinations

and for the car (problem 2) - 5 to the power of 4 = 5 x 5 x 5 x 5 = 625 car colour and accessory combinations?

Yup

Here's a good one - can you calculate the odds of winning the lottery?
So how many combinations of taking 6 numbers from 49?

14 million to 1 from memory.

MikeFish wrote:14 million to 1 from memory.

Yes i remember that statistic too when the lottery started here way back in the 90s (Nov 1994 i think)

Wow was it really that long ago?

Shouldn't it be 49 o the power of 6?
I make that 13.8 billion.