How many three digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 11?  Select
A) 14 B) 16 C) 18 D) 20 E) 22
A number is divisible by 11 when Difference of Sums of even place digits and odd place digits is either zero or a multiple of 11.   i.e. a 3-Digit Number abc will be divisible by 11 if (a+c) - b = 0 or multiple of 11   @b=1, a+c should be 1 or 12 i.e. (a,c) can be (5, 7), (7, 5) --- 2 cases   @b=2, a+c should be 2 or 13 i.e. (a,c) can be (6, 7), (7, 6) ---- 2 cases   @b=3, a+c should be 3 or 14 i.e. (a,c) can be (1, 2), (2, 1) ---- 2 cases   @b=4, a+c should be 4 or 15 i.e. (a,c) can be (1, 3), (3, 1) ---- 2 cases   @b=5, a+c should be 5 or 16 i.e. (a,c) can be (1, 4), (2, 3), (3, 2), (4, 1) ---- 4 cases   @b=6, a+c should be 6 or 17 i.e. (a,c) can be (1, 5), (2, 4), (4, 2), (5, 1) ---- 4 cases   @b=7, a+c should be 7 or 18 i.e. (a,c) can be (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) ---- 6 cases   Total Cases = 2+2+2+2+4+4+6= 
<gadget id="calculator">2+2+2+2+4+4+6</gadget>
<output>22</output>
22 cases   Answer: option 22
<result>E</result>
How many three digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 11?