Question

There are twenty-four $4$ -digit whole numbers that use each of the four digits $2, 4, 5,$ and $7$ exactly once. Listed in numerical order from smallest to largest, the number in the $17$ th position in the list is

$4527$

$5724$

$5742$

$7245$

$7524$

Solution:

Each leading digit accounts for $6$ of the $24$ numbers. Positions $1$ – $6$ begin with $2$ , positions $7$ – $12$ begin with $4$ , and positions $13$ – $18$ begin with $5$ .

So the $17$ th number is the $5$ th one beginning with $5$ : $5247, 5274, 5427, 5472, 5724$ . The fifth is $5724$ .

Thus, the correct answer is B .

1990 AMC 8 Problem 12

Solution:

Problem 12 in Other Years