Advanced Math Questions

1. Six children numbered with 1, 2, 3, 4, 5, 6 are sitting on six chairs, which are also numbered as 1, 2, 3, 4, 5 and 6. However, none of them are sitting on the chair indicating their own number. Find the expected number of swaps (e.g. 1 to 2 and 2 to 1) on the people so that they can ist on the chair with his own number.

2. Three elements are choosen from the set {1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987}. Find the number of distinct values of the sum of three three numbers.