Question

An ice-cream parlor sells sundaes with 3 different types of ice-cream and 4 different toppings. They have 8 flavors of ice-cream and 10 toppings for their customers to choose from. What is the probability that a customer orders a sundae including vanilla ice-cream and chocolate syrup?

Answer 1

`|\Omega|=\,_8C_3 \cdot\,_(10)C_4=(8!)/(3!5!)\cdot(10!)/(4!6!)=(6\cdot7\cdot8)/(2\cdot3)\cdot(7\cdot8\cdot9\cdot10)/(2\cdot3\cdot4)=11760\\|A|=\,_7C_2\cdot\, _9C_3=(7!)/(2!5!)\cdot (9!)/(3!6!)=(6\cdot7)/(2)\cdot (7\cdot8\cdot9)/(2\cdot3)=1764\\\\P(A)=(1764)/(11760)=(3)/(20)=15\%`