The alternating\:sum of the digits of 63\:195 is 6-3+1-9+5=0. In general, the alternating sum of the digits of a positive integer is found by taking its leftmost digit, subtracting the next digit to the right, adding the next digit to the right, then subtracting, and so on. A positive integer is divisible by 11 exactly when the alternating sum of its digits is divisible by 11. For example, 63\:195 is divisible by 11 since the alternating sum of its digits is equal to 0, and 0 is divisible by 11. Similarly, 92\:807 is divisible by 11 since the alternating sum of its digits is 22, but 60\:432 is not divisible by 11 since the alternating sum of its digits is 9.
Lynne forms a 7- digit integer by arranging the digits 1,2,3,4,5,6,7 in random order. What is the probability that the integer is divisible by 11?
Answer Choices
A. \frac{1}{35}
B. \frac{5}{42}
C. \frac{3}{35}
D. \frac{1}{42}
E. \frac{4}{35}