20 ice cream flavors and 20 toppings how many possible combinations are there

Question

all possible combinations 1 ice cream 20 toppings 2 scoops 20 toppings... what would be the formula to figure that out

Answer 1

wow  fourth grade math..

"are you smarter than a fifth grader">??

☺ 40 ??☺

or the simple 400

or are you going mix the 400 with double dutch

can we mix three of each ??

where do you end

"I am not smarter than I Don't K.."

Edit

now he changes the rules..???

Answer 2

can the ice cream have more than one topping?

can the ice cream or topping stand alone? (as retarded as that sounds)

or simply 1 ice cream needs one 1 topping, if so then 400

Answer 3

8000

Answer 4

420 .20 WIHTOUT TOPPINGS

Answer 5

401.  The 1 is without any topping.  :=)

Answer 6

If you include double flavors the first flavor could combine in 20 different ways, the second flavor could combine with 19 flavors(everything but the first) and so on.  That gives you a total of 210 ice cream combos.  Then with one topping and 20 possibilities you get 210x20 which is 4200 possibilities. With two toppings including just using just one it would be 210x210 so it would be 44100

This is the type of question you might get in a Statistics class...

Answer 7

400 And If You Count Nothing As A Topping 401

Answer 8

I guess the best way to figure out that one is to multiply 20 times 20.

Answer 9

in your example you state 2 scoops 20 toppings so lets call 2 scoops the max # of scoops and any combination of  up to 20 toppings.

icecream * toppings

20 possible flavours of either 1 or 2 scoops

1 scoop = 20 ( no icecream is not an option )

2 scoops ( could be strawberry strawberry ) = 20_C_2 + 20

( 20_C_2 does not include 2 scoops of same flavour so we have to add 20 to account for that )

so total icecream combinations ( with double scoops of same flavour but counting vanilla on top of chocolate as the SAME as chocolate ontop of vanilla ) = 20+20+20_C_2 = 20+20+190=230

230 possible 1 or 2 scoop combinations WITH double scoops of same falvour ( if you dont want to include this then subtract 20 )

now for topping combinations.

could be 1 topping, could be 2 toppings...etc. but we will say that doubleing 1 topping is not allowed ( 2wice as much chocolate syrup still counts as just 1 chocolate syrup ) also the order on which the topping are added is not accounted for.

so for toppings we have 20 ( 1 topping ) + 20_C_2 ( 2 topping ) + 20_C_3 ( 3 topping) + 20_C_4 ( 4 topping )...etc.

20_C_0 ( no toppings ) = 20_C_20 ( all toppings )  = 1

20_C_1 ( 1 topping ) = 20_C_19 ( 19 toppings )  =  20

etc.

for a total of 1*2  +  20*2  +  190*2  +  1140*2  +  4845*2........+167960*2 + 184756*1 ( 10 toppings )

so there are 1 048 534 possible topping combinations ( no doubling up of toppings )

this gives us 1 048 534  *  230  ( for each icecream combination 1 of the topping combinations may be chosen )

= 241 162 820 possible 1 or 2 scoop icecream cones with anywhere from 0 to 20 toppings.

if 1 or 2 scoops were permitted and 0,1, or 2 toppings were permitted  and we could double up on icecream flavours or toppings it would be

icecream = 20 + (20_C_2) + 20(double scoops of same flavour )

topping = 1 ( no topping )  +  20 ( 1 topping ) + 20 ( double topping ) + (20_C_2) ( 2 different toppings )

=230 * 231 = 53 130 possible combinations.