An ice cream stand has nine different flavours. A group of children come to the stand and each buys a double scoop cone with two flavours of ice cream. If none of the children choose the same combination of flavours, and every different combination of flavours is chosen, how many children are there?
FLAVOURS 1 Vanilla 2 Maple 3 Chocolate 4 Tiger 5 Raspberry 6 Strawberry 7 Coffee 8 Moon Mist 9 Cherry Vanilla
There are 45 different combinations of ice cream they can make. I know this because I wrote them all out and I did the math as well. The math way is that since they are 9 different flavours of ice cream I did 9+8+7+6+5+4+3+2+1. The reason I did this is because i found 9 different combinations for the vanilla flavour. Then i found only 8 combinations for maple flavour. the reason for this is because i already did vanilla and maple together maple and vanilla again would be the same thing so i took one combination out. then when i found 6 different combinations for chocolate because i did vanilla-chocolate and maple-chocolate already so i took 2 out. the pattern keeps going on and on so i did 9+8+7+6+5+4+3+2+1.
ReplyDeleteTo find the answer i drew a tree diagram. I started off with Vanilla paired with VAnilla. Then Vanilla and Maple, Vanilla Chocolate. I found they were nine different combinations of Vanilla. Next, I did Maple, and found there were only 8 combinations. Next, Chocolate, Tiger,Rasberry,Strawberry, Moon Mist, and Cherry Vanilla. Each one i did there was one combination less. So 9+8+7+6+5+4+3+2+1= 45. So, i got the same answer as George but ina different way.
ReplyDeleteThe answer is 45 children. I drew a tree diagram to find the answer. First I paired the combinations with vanilla, there are 9. Then maple there are 8. Each flavour the number decreased by 1. 9+8+7+6+5+4+3+2+1=45.
ReplyDeleteI found the answer by drawing a tree diagram. I started off with vanilla, and I paired it up with the 8 other flavors. There were 9 flavors in total. I did not pair one scoop of vanilla with another scoop of vanilla because I noticed that it said that each scoop had two flavors of ice cream, not one. I did the same thing with maple, except I only found 7 flavors because I had already paired maple with vanilla. Then i drew tree diagrams for every flavor, and each time the amount of combinations decreased by one. So I added up the total amount of combinations from the tree diagram: 8+7+6+5+4+3+2+1=36. So in total there are 36 combinations. And the answer depends on whether you count the order of the scoops.
ReplyDeleteHave a great Tuesday,
~*Evy*~
Sorry I meant that each cone had two flavors ice cream.
ReplyDeleteOr i guess if you can pair a vanilla with a vanilla there would be 45 children. 9+8+7+6+5+4+3+2+1=45. Depends on how you look at it.
ReplyDeletewhat i did was make a tree diagram. I started with vanilla and there were 9 combinations then i did maple, there were 8 combinations i did two more which were chocolate and tiger and realized there was a pattern it went down by one each time... vanilla=9 maple=8 chocolate=7 tiger=6 etc. so i added them up: 9+8+7+6+5+4+3+2+1=45! so my final answer is 45
ReplyDeletei used a tree diagram to figure it out, my final answer is:45kids. the first thing i did was vanila V+CV,V+M,V+CH,V+T,V+S,V+R,V+CO,V+MM =8 different pairs of icecream. then i did all the other combo's without repeting a number. each time i started a new combo, the number of avalible icecream flavors, decreased by 1. i could of added it up for 9 to 1, but to make sure my answer was correct i kept going with my tree diagrams. and i ended up with 45 children.
ReplyDeleteDictionary: CV=cherry vanila, CH= chocolate, CO= coffee, V= vanila, R= rasberry, M=maple, T= tiger, s= strawberry, mm=moon mist.
Adele
I pretty much did the same as everyone. I dind't make a tree diagram I just counted all the combinations that didn't repeat. Like I didn't do vanilla+chocolate and chocolate+vanilla. I added up all the combinations to get 45. So there must have been 45 kids. Thats alot for one ice cream stand to handle...
ReplyDeleteThe answer I got (like everyone else) was 45. I didn't make a chart, but wrote down all the combanations. Since there can not be vanilla&coffee, then coffee&vanilla, there were 9 vanilla combos. Then for chocolate I found that there were 8 combos. I did this for all of them and added them. 9+8+7+6+5+4+3+2+1=45
ReplyDeleteThe answer i got is 36. I used the combination formula which is N factorial divided by R factorial times (N-R) factorial and the answer i got is 36. N = 9 so it is 1x2x3x4x5x6x7x8x9 = 9 factorial. R = 2 scoops, 1x2 = 2 factorial. N - R = 9 - 2 = 7 so the equation is: 1x2x3x4x5x6x7x8x9 / 1x2 x 1x2x3x4x5x6x7 so when we get rid of 1x2x3x4x5x6x7 we get rid of it from both so the next equation is 8x9 / 1x2 8x9 = 72 divided by 2 = 36. that is the answer i got.
ReplyDeletei knew this same question from some other math challenge thing so lets say i used a tree diagram. i know from other math things is that it goes down my one each time ex. u cannot pair chocolate and maple and maple and chocolate. so how i figured it out was by adding 9+8+7+6+5+4+2+1=b45. there are 45 flavours
ReplyDeleteI counted them all constantly counted them all subtracting one each time until i was out of flavors to count. In the end I got 45!
ReplyDelete45 children is my answer.
PS i am devon.
The easiest way to put it is this:
ReplyDeleteTree diagram without double flavours, answer: 45.
The answer is 36 kids. 8+7+6+5+4+3+2+1=36.
ReplyDeleteThe answer I got is 36. For Vanilla the kids could choose 8 combinations of two scoops, for Maple - 7, for Chocolate -6, for Tiger -5, Rasperry - 4, Strawberry - 3, Coffee - 2, Moon mist - 1 and Cherry Vanilla - 0. If you add all those numbers up you get 36.
ReplyDeleteThere were 36 children I was gunna say 45 but then i reread to find out if you could have a vinilla and a vanilla or any of the same type of ice cream but you CAN'T. CAN YOU.Em$$$
ReplyDelete