## 4-Digit Numbers Divisible by 7

Given the digits $1,3,6$, and $9$, find the probability that a four-digit number formed by using each of them only once is divisible by $7$.
Source: NCTM Mathematics Teacher, February 2008

Solution
There are $4\times 3\times 2\times 1=24$ possible four-digit numbers using $1,3,6,9$ each only once
$1369,1396,1639,1693,1936,1963$
$3169,3196,\underline{3619},3691,3916,3961$
$\underline{6139},6193,6319,\underline{6391},6913,6931$
$9136,\underline{9163},9316,9361,9613,9631$
Numbers divisible by $7$ are $3619,6139,6391,9163$
Probability = $4/24=1/6$.

Answer: $1/6$