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In how many ways, one white and one black rook can be placed on a chessboard so that they are never in an attacking position?

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Important Questions on Permutations and Combinations

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How many 6-digit numbers have all their digits either all odd or all even?
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On a triangle ABC, on the side AB, 5 points are marked, 6 points are marked on the side BC and 3 points are marked on the side AC (none of the points being the vertex of the triangle). How many triangles can be made by using these points?
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In the Sunita Building in Mumbai, there are 12 floors plus the ground floor. 9 people get into the lift of the building on the ground floor. The lift does not stop on the first floor. If 2, 3 and 4 people alight from the lift on its upward journey, then in how many ways can they do so? (Assume they alight on different floors.)
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There are 40 doctors in the surgical department of the AIIMS. In how many ways can they be arranged to form a team with 1 surgeon and 4 assistant.
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How many five-digit numbers, which do not contain identical digits, can be written by means of the digits 1, 2, 3, 4, 5, 6, 7, 8, 9?

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How many different four-digit numbers can be written using 1, 2, 3, 4, 5, 6, 7, 8 only once such that the number  2 is contained once?
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The number of ways in which four particular persons A, B, C, D and six more persons can stand in a queue so that  A always stands before B, B always before C and C always before D is: