The sundae bar in the Starkiller Base lunchroom has 20 different toppings, and n

Question

The sundae bar in the Starkiller Base lunchroom has 20 different toppings, and normally 10 different flavors of icecream. Due to a recent attack by the Resistance, Starkiller Base only has vanilla ice cream, How many distinct sundaes can be made by radar technician Matt? How does the answer to Part (a) change if the other 9 flavors of ice cream become available (in addition to vanilla)? Assume that only 1 flavor of ice cream is used in each sundae. How many distinct sundaes can be made if 3 flavor of ice cream are used in each sundae?

Explanation / Answer

4.) (a) Assuming only one topping is used in one sundae bar

So, Number of different combinations = 1C1 * 10C1 = 10

(b) Assuming only one topping is used in one sundae bar

Number of flavours = 10

Number of Toppings = 10

We can choose on only one flavor and one topping for one sundae

Number of distinct sundae = 10C1 * 10C1 = 10 * 10 = 100

(c) Assuming only one topping is used in one sundae bar

Number of flavours = 10

Number of Toppings = 10

We can choose 3 flavor and one topping for one sundae

Number of distinct sundae = 10C3 * 10C1 = 120 * 10 = 1200

5.)

(a) For scoring exactly 3 points we need all 3 cards to be red.

P( 3 reds) = (26/52) * (25/51) * (24/50)

= 0.117

(b) From the table above we can see that we can never score exactly 2 points.

Hence P(Exactly 2 points) = 0

(c) Fromt the table we can see that for scoring exactly 1 point we need 2 Red and 1 Black.

P(2 Red and 1 Black) = (26/52)*(25/51)*(26/50)

= 0.127

Cards Points 3 Red, 0 Black 3 2 Red, 1 Black 1 1 Red, 2 Black -1 0 Red, 3 Black -3

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