Count the possibilities, not just the objects.
A few small combinations worth drawing out.
Ten questions, with the answers explained. Try them in your head, then open each answer when you're ready.
Play this quiz →QUESTION 1 / 10
You have three shirts and two pairs of trousers. How many shirt-and-trouser combinations can you make?
- Three
- Five
- Nine
- Six
Show answer & explanation+
Six
Each of three shirts can pair with either of two trousers: three times two is six.
QUESTION 2 / 10
Four people each shake hands with every other person once. How many handshakes occur?
- Eight
- Twelve
- Six
- Four
Show answer & explanation+
Six
Each unique pair shakes once. Four times three divided by two gives six.
QUESTION 3 / 10
You choose one of two soups and one of three mains. How many different two-course orders are possible?
- Five
- Nine
- Six
- Three
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Six
Each soup pairs with three mains, giving two times three orders.
QUESTION 4 / 10
How many different orders can three distinct books be placed in a row?
- Three
- Four
- Six
- Nine
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Six
There are three choices for the first position, two for the second, and one for the last.
QUESTION 5 / 10
How many two-letter codes can be made from A and B if repetition is allowed?
- Two
- Three
- Six
- Four
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Four
The codes are AA, AB, BA, and BB.
QUESTION 6 / 10
How many distinct pairs can you choose from three different friends?
- Four
- Two
- Six
- Three
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Three
For friends A, B, and C, the pairs are AB, AC, and BC.
QUESTION 7 / 10
A cafe offers two cup sizes and four drink flavors. How many size-flavor choices are possible?
- Eight
- Ten
- Six
- Four
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Eight
Each of two sizes has four flavor options, giving eight choices.
QUESTION 8 / 10
How many distinct three-digit codes use 1, 2, and 3 exactly once each?
- Six
- Three
- Twenty-seven
- Nine
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Six
Three choices, then two, then one gives six permutations.
QUESTION 9 / 10
Five people each send one postcard to every other person. How many postcards are sent?
- Fifteen
- Twenty
- Twenty-five
- Ten
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Twenty
Each of five people sends four postcards, making twenty in total.
QUESTION 10 / 10
You may choose either tea, coffee, or juice, with or without ice. How many choices are there?
- Three
- Nine
- Five
- Six
Show answer & explanation+
Six
Three drink choices each have two ice options.