Question

Tino's Ice Cream Shoppe features seven flavors: vanilla, chocolate, pistachio, coconut, blackberry, lemon, and saffron. Tino will gladly make you an ice cream shake featuring any two scoops you want (not necessarily of different flavors). For example, you can order blackberry-vanilla, or pistachio-saffron, or even chocolate-chocolate. Since the scoops are just going into the blender anyway, the order of the scoops doesn't matter: there's no difference between blackberry-vanilla and vanilla-blackberry.

How many different shakes can you order?

Answer 1

28 different shakes can be made

Answer 2

The number of ways different shakes can be ordered in 21 ways.

What is a combination?

"A combination is a way of selecting items from a collection where the order of selection does not matter".

For the given situation,

Seven flavors of ice cream are vanilla, chocolate, pistachio, coconut, blackberry, lemon, and saffron, n=7.

The Ice cream shake is made in two scoops, r=2.

The formula for combinations is given by

The number of different shakes that can be ordered is given by nCr

$nCr = \frac{n!}{r!(n-r)!}$

⇒ $7C2 = \frac{7!}{2!(7-2)!}$

⇒ $7C2=\frac{7!}{2!5!}$

⇒ $7C2=\frac{5040}{(2)(120)}$

⇒ $7C2=21$

Hence we can conclude that the number of ways different shakes can be ordered in 21 ways.

Learn more about combinations here

https://brainly.com/question/26818789

#SPJ2