Question

Find the number of ways to purchase 5 different kinds of juices from a selection of 10 juices

Answer 1

Formula for combinations:
(n!)/(r!(n-r)!)

For you, this is:
10!/(5!(10-5)!) = 10!/5!5! = (10•9•8•7•6•5•4•3•2)/(5•4•3•2)(5•4•3•2) = (10•9•8•7•6)/(5•4•3•2) = 30240/120=252 different ways.