There are 20

I did this with a 3 by 3 grid - not including headings    (like a times table grid)

The headings along the top are left right and total

The headings down the side are like jazz, dislike Jazz and total

Then i filled in what I was given and worked out the rest.   

12 are right-handed

Of these....2 dislike jazz

So.....10 must like jazz

And since 15 total like jazz....5 of those must be left-handed