Question

In how many ways can you choose 3 kinds of ice cream and 2 kinds of toppings from a dessert buffet with 10 differnt kinds of ice cream and 6 kinds of toppings

Answer 1

we know that
the formula of combinations is
C=[n!]/[(n-r)!*r!]
where
n-------------> the total number of objects
r------------- > number that you choose to arrange
ice creams
n=10
r=3
C=[10!]/[(7)!*3!]=C=[10*9*8]/[3*2*1]=120
toppings
n=6
r=2
C=[6!]/[(4)!*2!]=C=[6*5]/[2*1]=15

the answer is (120)*(15)=1800 ways