4. I went shopping for a used c One car I liked was priced at $3,211, another ca

Question

4. I went shopping for a used c One car I liked was priced at $3,211, another car at $2,311, and anot noticed that if you added all of the the digits of each price, they added to to the owner, Hans, and he told me that every car was priced liket her at $4,111.I 7. I talked hat; the sum of igits in the price was 7. Every car had a different price, and he never used a zero in the price. None of the cars cost more than $15,000, and none cost less than $1,000. How many different prices did Hans have available to him?

Explanation / Answer

The combination for prices between $ 1000 and $ 9999 are

(1,1,1,4) , (1,1,2,3) and (1,2,2,2)

No of different prices with (1,1,1,4) = 4! ÷ 3! = 4

No of different prices with (1,1,2,3) = 4! ÷ 2! = 12

No of different prices with (1,2,2,2) = 4! ÷ 3! = 4

The combination for prices between $ 10000 and $ 15000 are

(1,1,1,1,3) and (1,1,1,2,2)

However we want prices which are less than 15000, Thus we fix '1' at the first place:

No of different prices with (1,1,1,1,3) = 4! ÷ 3! = 4

No of different prices with (1,1,1,2,2) = 4! ÷ (2! * 2!) = 6

Total different prices = 4 + 12 + 4 + 4 + 6 = 30

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