How many two digit whole numbers can be written as the sum of two different single digit whole numbers? Lots of points, and will
2 answers:
You want . We can go about this by casework. WLOG x=9, we have 8 digits: 1-8. With x=8 we have 2-9, but we already counted 8 and we already considered the 9 case, so we have 2-7 actually, which will give us 6 numbers. With x=7, with the same logic we are only looking for the numbers 3-6 which there are 4 of. With x=6, you are looking for the numbers 4-5 which are 2. With x=5 run out of numbers to pick. The numbers are indistinguishable and it does not matter whether we use x or y so we just have to ad up the cases we already have to get: 20.
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Answer:
The traveler can plan such a tour in 3003 ways.
Step-by-step explanation:
The order that the cities are chosen is not important, since it is chosen by the company and not by the traveler. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this problem, we have that:
Combinations of 5 cities from a set of 15. So
The traveler can plan such a tour in 3003 ways.