The board of directors of a company decides to promote 3 of its 10 senior staff members to the position of first vice president, second vice president, and third vice president. In how many ways can this promotion be made?

The sum of the angles in a triangle is 180°. this is called the angle-sum property.the sum of the lengths of any two sides of a triangle is greater than the length of the third side. similarly, the difference between the lengths of any two sides of a triangle is less than the length of the third side.the side opposite to the largest angle is the longest side of the triangle and the side opposite to the smallest angle is the shortest side of the triangle.