1) Make your own sundae: 4 Ice Cream Flavors and 6 Toppings A) Sundaes are possi
ID: 2950881 • Letter: 1
Question
1) Make your own sundae: 4 Ice Cream Flavors and 6 ToppingsA) Sundaes are possible using 1 flavor of ice cream and 3 differenttoppings?
4C1 = 4
6C3 = 120 * 4 = 480
B) Sundaes are possible using 1 flavor of ice cream and 0 to 6toppings?
4*6P6 = 4*6! = 2,880
C) Different comb. of flavors of 3 scoops of ice cream are possibleif it is permissible to make all 3 scoops the same flavor?
4P3 = 24, or is the 64, 4*4*4?
2) How many different varieties of pizza can be made if you have:small, medium, large size; thin n' crispy, hand tossed, or pancrust; and 12 toppings(cheese automatic), from which you may selectfrom 0 to 12?
3P1 = 3
4P1 = 4
12P1 = 12*4*3 = 144
And can someone please explain permutation and combination. I knowpermutation, order matters and combination it doesn't, but I stillget confused on which one to use.
Explanation / Answer
A) Exactly 1 ice cream flavor and exactly 3 toppings. C(4, 1) = 4 C(6, 3) = 20 4 * 20 = 80 B) Exactly 1 flavor and 0 to 6 toppings C(4, 1) = 4 C(6, 6) + C(6, 5) + ... C(6, 0) = 2^6 = 64 4 * 64 = 256 2) 3 pizza sizes 3 types of pizza C(12,0) + C(12, 1) + ... C(12, 12) = 2^12 = 4096 3*3*4096 36864 C(n, k) is the number of ways of choosing k items from a list of nitems (i.e. order doesn't matter). P(n, k) is the number ofways of choosing k items from a list of n items when order doesmatter. P(n, k) = n! / (n-k)! = n * (n-1) * (n-2) * ... * (n-k+1) C(n, k) = n! / (k! * (n-k)!) = P(n, k) / k! In summary, use nCr when AB = BA (i.e. if we apply two toppings,pepperoni and meatball is the same as meatball andpepperoni). Use nPr when AB does not equal BA. Forinstance, if we have a game where heads-tails does not have thesame payout of tails-heads, then we would need to use nPr. Note: I have intentionally left 1C to you for practice. It'sa bit tricky so be careful. If you have difficulties with it,post again with your problems.
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