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Question 269159: Sandy typed a positive six-digit integer, but the two 9s she typed didn’t show. If 2010 appeared, how many different positive six-digit integers could she have typed? One such integer to include is 920910.
Answer by AnlytcPhil(1810)   (Show Source):
You can put this solution on YOUR website! Sandy typed a positive six-digit integer, but the two 9s she typed didn’t show. If 2010 appeared, how many different positive six-digit integers could she have typed? One such integer to include is 920910.
There are 5 positions into each of the 9's could have
supposed to have been.
1. before the 2
2. between the 2 and the 1st 0
3. between the 1st 0 and the 1
4. between the 1 and the second 0
5. after the second 0.
There are two cases:
1. When the two 9's are in different positions
5C2
2. When both 9's are together in the same position:
5C1
That's 5C2 + 5C1 = 10 + 5 = 15
Here are the 5C2 or 10 where the 9's are in different
positions, not right together:
1. 929010
2. 920910
3. 920190
4. 920109
5. 290910
6. 290190
7. 290109
8. 209190
9. 209109
10. 201909
And here are the 5C1 or the other 5, where the 9's
are together in the same position.
11. 992010
12. 299010
13. 209910
14. 201990
15. 201099
So there are indeed 15 in all.
Edwin
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