randomstudent0
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The coffee machine in our office offers a choice of regular or decaffeinated coffee; black or with one of three sorts of milk (full, semi-skimmed, skimmed); and, for those who want
sweetening, either one or two spoonfuls of sugar or one or two non-sugar sweetening tablets.

How many different kinds of coffee can be made?
A 11
B 24
C 32
D 40
E 48

The answer is D and methods I have seen for this question involve literally writing every single possible kind of coffee and counting them - does anyone know if there is a quicker way to do these kinds of questions?
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lordaxil
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The key is to realise the sweetener is optional, and therefore there are 5 choices in the last step. 2 \times 4 \times 5 = 40
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Ice.Log
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(Original post by randomstudent0)
The coffee machine in our office offers a choice of regular or decaffeinated coffee; black or with one of three sorts of milk (full, semi-skimmed, skimmed); and, for those who want
sweetening, either one or two spoonfuls of sugar or one or two non-sugar sweetening tablets.

How many different kinds of coffee can be made?
A 11
B 24
C 32
D 40
E 48

The answer is D and methods I have seen for this question involve literally writing every single possible kind of coffee and counting them - does anyone know if there is a quicker way to do these kinds of questions?
I have a slightly simpler solution for this problem (though it may not be perfect - yr11 btw):

1• We know each possible combo must have Regular (R) or Decaffeinated (D).
And must have either Black (B), Full milk (F), Semi- skimmed (Ss) or skimmed (S).

2• Instead of writing out each combo, work out all the possibilities for R or D, then multiply it by 2.

3• There are 4 base combos for R. RB, RF, RSs, and RS.

4• There are four more options which will bring about four more combos for each: 1 spoon sugar, 2 spoon sugar, 1 tablet, 2 tablets.

5• So: base combos=4,
1spoon sugar =4,
2 spoon sugar=4,
1 tablet=4,
2 tablets=4 combinations.

4+4+4+4+4=20 for Regular. Multiply 20 by 2 for the Decaffeinated section and you get 40 in total.
Hope this helps.
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DeBeauvoir2
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2 options for coffee - so 2
For each of those there are 4 milkiness options - so 2x4
For each of those there are 5 sweetness options - so (2x4x5)

If you did GCSE maths visualise a probability tree
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Ice.Log
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(Original post by DeBeauvoir2)
2 options for coffee - so 2
For each of those there are 4 milkiness options - so 2x4
For each of those there are 5 sweetness options - so (2x4x5)

If you did GCSE maths visualise a probability tree
Ugh, why do I always overcomplicate things. Better brush up on my maths again
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DeBeauvoir2
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(Original post by Ice.Log)
Ugh, why do I always overcomplicate things. Better brush up on my maths again
Gets easier
What are you applying for?
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Ice.Log
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(Original post by DeBeauvoir2)
Gets easier
What are you applying for?
Y11 but Engineering at Cambridge, Design Engineering at Imperial and 3 more RG unis next year.
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DeBeauvoir2
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(Original post by Ice.Log)
Y11 but Engineering at Cambridge, Design Engineering at Imperial and 3 more RG unis next year.
In that case you probably don’t need the TSA if you dont know - it’s just a handful of oxford courses, land economy and cambridge, and esps at UCL
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Ice.Log
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(Original post by DeBeauvoir2)
In that case you probably don’t need the TSA if you dont know - it’s just a handful of oxford courses, land economy and cambridge, and esps at UCL
Yh, but some of the questions are kinda interesting to answer.
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DeBeauvoir2
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(Original post by Ice.Log)
Yh, but some of the questions are kinda interesting to answer.
I agree
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randomstudent0
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(Original post by Ice.Log)
I have a slightly simpler solution for this problem (though it may not be perfect - yr11 btw):

1• We know each possible combo must have Regular (R) or Decaffeinated (D).
And must have either Black (B), Full milk (F), Semi- skimmed (Ss) or skimmed (S).

2• Instead of writing out each combo, work out all the possibilities for R or D, then multiply it by 2.

3• There are 4 base combos for R. RB, RF, RSs, and RS.

4• There are four more options which will bring about four more combos for each: 1 spoon sugar, 2 spoon sugar, 1 tablet, 2 tablets.

5• So: base combos=4,
1spoon sugar =4,
2 spoon sugar=4,
1 tablet=4,
2 tablets=4 combinations.

4+4+4+4+4=20 for Regular. Multiply 20 by 2 for the Decaffeinated section and you get 40 in total.
Hope this helps.
thank you!
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randomstudent0
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(Original post by DeBeauvoir2)
2 options for coffee - so 2
For each of those there are 4 milkiness options - so 2x4
For each of those there are 5 sweetness options - so (2x4x5)

If you did GCSE maths visualise a probability tree
how did I forget probability trees exist lol thank you!
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