First Figure out
How many ways there are for a user to get any music out of the horses ?
No. of Horses Possibilities
1 4 (h1, h2, h3, h4)
2 6 ( h1h2 , h1h3, h1h4 , h2,h3, h2h4 , h3h4 )
3 4 (h1h2h3 , h1h2h4 , h1h3h4 , h2h3h4 )
4 1 (h1h2h3h4)
Total : 15
Another way to think is that the user has a choice to make each horse , to choose it or leave it.And the user has to make this choice 4 times , so total ways of making all possible choices are
2x2x2x2 = 16
this includes the scenario where the user rejects all horses , however the question demands that the music is created so we subtract 1 from this and we get 15 as the answer.
2x2x2x2 how what
Imagine you have only 2 pants and 2 shirts and civil society demands that you are dressed in at least on of each item. How many different looks can you generate
for starters you could make a table of all possible ways , being systematic would help.
Pant1 Shirt 1
Pant 1 Shirt 2
Pant 2 Shirt 1
Pant2 Shirt 2
or
There are 2 ways of choosing a shirt and 2 ways of choosing a shirt and you have to choose for both. For each choice you make in the pants area there are two choice more so total choices are 2×2
3 shirts and 5 pants and 4 ties
3 choices for Shirts for each shirt you choose then there are 5 more choices for pants and for each shirt pant pair their are further 4 choices for the Tie
3x4x5 = 60
I could have also thought of starting with pants and thinking of possible shirt tie pairs for each pant. 3 shirts and 4 ties there are 12 different pairs possible. i.e after choosing a pant i still have 12 possible ways of going for Shir-tie
5×12 = 60
If there are A ways of doing X and B ways of doing Z then the total number of ways of doing X and Z are A X B
Now imagine you have 3 formal pants 4 party pants and 5 formal shirts and 6 party shirts how many ways can you dress your self if formal pants go only with formal shirts and party pants go with party shirts?
In essence you could either dress formal OR dress for a party
formal dressing options
3 x 5 = 15
party dressing Options
4 x 6 = 24
total dressing options = 24 + 15
A ways of Doing X and B ways of doing Z , total ways of doing X OR Z is A+B