Permutations an...

The number of ways in which 3 friends can stay in 2 hotels is

The number of ways in which Mr. A can give 2 hotels to his 3 rows is

A five letter word is to be formed such that the letters appearing in the odd numbered positions are taken from the letters which appear without repetition in the word MATHEMATICS. Further, the letters appearing in the even numbered positions taken from the letters which appear with repetitions in the same word MATHEMATICS. The number of different ways in which the five letter word be formed is

The 10 students of Batch B feel they have some conceptual doubt on ‘Circular Permutation’. Mr. Sood called them in discussion room and asked them to sit down around a circular table which is surrounded by 13 chairs. Mr. Sood told that his adjacent seat should not remain empty. The number of ways in which the students can sit around a round table if Mr. Sood also sits on a chair is

A person invites a party of 10 friends at dinner and place them
(i) 5 at one round table, 5 at the other round table
(ii) 4 at one round table and 6 at other around table.
The ratio of number of circular permutations of case (i) to case (ii) is

Line L₁ contains l₁ points and line L₂ contains l₂ points. If the points on L₁are joined to the points on L₂, then number of points of intersection of new lines, is

The number of points in the cartesian plane with integral co-ordinates satisfy the inequalities |x| ≤ K, |y| ≤ K, |x – y| ≤ K is

The sides AB, BC and CA of a triangle ABC have a, b and c interior points on them respectively. Then the number of triangles that can be constructed using these interior points as vertical, is

The total number of triangles which can be formed by using above l₁ + l₂ points and the point of intersection of L₁ and L₂ is

A watch of meritorius students of the coaching institute is to be formed. For this a student must obtain at least 80% aggregate marks in a test of Physics, Chemistry and Math. (M.M. = 100 each).
The number of ways in which a student can qualify for the batch of meritorius students is