2002 AMC 8 Problems/Problem 19

Problem

How many whole numbers between 99 and 999 contain exactly one 0?

$\text{(A)}\ 72\qquad\text{(B)}\ 90\qquad\text{(C)}\ 144\qquad\text{(D)}\ 162\qquad\text{(E)}\ 180$

Solution

This list includes all the three digit whole numbers except 999. Because the hundreds digit cannot be 0, there are $2$ ways to choose whether the tens digit or the ones digit is equal to 0. Then for the two remaining places, there are $9$ ways to choose each digit. This gives a total of $(2)(9)(9)=\boxed{\text{(D)}\ 162}$ . or we can Numbers with exactly one zero have the form $\_ 0 \_$ or $\_ \_ 0$ , where the blanks are not zeros. There are $(9\cdot1\cdot9)+(9\cdot9\cdot1) = 81+81 = \boxed{162}$ such numbers.-Alcumus(all credit to Alcumus, not me)

2002 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 18	Followed by Problem 20
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2002 AMC 8 Problems/Problem 19

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