The exact question is:
b) Sandra wishes to buy some applications (apps) for her smartphone but she only has enough money for 5 apps in total. There are 3 train apps, 6 social network apps and 14 games apps available. Sandra wants to have at least 1 of each type of app. Find the number of different possible selections of 5 apps that Sandra can choose?
How I approached this question :
As we need to choose 1 from each catagory, the first three apps can be choosen in :
3 x 6 x 14 = 252 ways.
Now, for the remaining 2 apps, we can choose from the 20 apps (3 + 6 + 14 - the installed 3 apps)
So, number of combinations should be 20C2 = 190, so finally the answer I got to was 3 x 6 x 14 x 190 = 47880 which is wrong, the answer is 13839 ways. After trying another method I got 13839 but, I need to know why this method is wrong. Can anyone explain this?