Difference between revisions of "2002 AMC 8 Problems/Problem 19"
Mrdavid445 (talk | contribs) (Created page with "How many whole numbers between 99 and 999 contain exactly one 0? <math> \text{(A)}\ 72\qquad\text{(B)}\ 90\qquad\text{(C)}\ 144\qquad\text{(D)}\ 162\qquad\text{(E)}\ 180 </math>") |
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| + | ==Problem== | ||
| + | |||
How many whole numbers between 99 and 999 contain exactly one 0? | How many whole numbers between 99 and 999 contain exactly one 0? | ||
<math> \text{(A)}\ 72\qquad\text{(B)}\ 90\qquad\text{(C)}\ 144\qquad\text{(D)}\ 162\qquad\text{(E)}\ 180 </math> | <math> \text{(A)}\ 72\qquad\text{(B)}\ 90\qquad\text{(C)}\ 144\qquad\text{(D)}\ 162\qquad\text{(E)}\ 180 </math> | ||
| + | |||
| + | ==Solution== | ||
| + | This list includes all the three digit whole numbers except 999. Because the hundreds digit cannot be 0, there are <math>2</math> ways to choose whether the tens digit or the ones digit is equal to 0. Then for the two remaining places, there are <math>9</math> ways to choose each digit. This gives a total of <math>(2)(9)(9)=\boxed{\text{(D)}\ 162}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2002|num-b=18|num-a=20}} | ||
Revision as of 19:10, 23 December 2012
Problem
How many whole numbers between 99 and 999 contain exactly one 0?
Solution
This list includes all the three digit whole numbers except 999. Because the hundreds digit cannot be 0, there are 
ways to choose whether the tens digit or the ones digit is equal to 0. Then for the two remaining places, there are 
ways to choose each digit. This gives a total of 
.
See Also
| 2002 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 18 |
Followed by Problem 20 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
