11 Plus Exams Forum

Please can someone show me how to answer this question.
"Craig is arranging plates of food. He has 3 types of sandwiches, 2 types of cake and 4 types of biscuits. Which show the number of possible combinations of sandwich, cake and biscuits on a plate. "
A: (3x2)+(3x4)
B: 3x2x4
C:(3x4)+(2x4)
D: 3+2+4
E:(2x3)+(2x4)
Thankyou

Suppose he just had three different types of sandwich to put on each plate. Call them flavours A, B or C. There would then be three possibilities.

Now suppose he had three types of sandwich and two types of cake. Call them D and E. On plates with sandwich A he could put either type of cake, giving AD or AE. Similarly the other plates with B and C on also have 2 possibilities. So for just cakes and sandwiches the are 2*3 possibilities.

For each of the six combinations of sandwiches and cakes there are 4 different biscuits. Hopefully you should see where this is going to give answer B.

This isn't algebra by the way - it's part of statistics.

If teaching this, then start simpler.

Chocolate cake or lemon cake, 1 drink - only 2 choices

2 cakes, lemonade or apple juice - 4 choices

Continue to add choices and if DC is struggling then do this physically with food from the cupboard.

The question doesn't specify only one sandwich, cake and biscuit type on each plate, so if Craig was a bit greedy then there could be more combinations, eg could have one sandwich, one cake and two biscuits on each plate etc.......

Yes - this is from a gl practice paper and I have always been a bit puzzled by this question as it does not say that you have to put one type of sandwich and one type of cake and one type of biscuit on each plate. If it did, then giving them letters and listing the possibilities will help you see the answer. But if you are puzzling whether you can just eat biscuits, for example, or have a bit of everything, you can't answer in 1 minute or so as needed.