Permutations and Combinations

A college offers 5 course in the morning and 3 in evening. The number of ways a student can select exactly one course, either in the morning or in the evening, is

If $n=12,r=12$, then $\dfrac{n!}{r!(n-r)!}=$

A college offers 6 courses in the morning and 4 in the evening. The possible number of choices with the student if he wants to study one course in the morning and one in the evening is

In a test, there are 7 questions of the type 'True or False'. No student got all the answers correct. If the sequence of answers for every student is unique, then the maximum number of students who appeared for the test is . . .

Given 4 flags of different colours, how many different signals can be generated, if a signal requires the use of 2 flags one below the other?

In a steamer there are stalls for 15 animals and there are cows, horses and calves (not less than 15 of each) ready to be shipped. The total number of ways in which ship load can be made is

The number of ways in which we can put 5 letters in 10 letter boxes is

If 20 points are marked on a circle, then the number of chords which can be drawn are

Ten points are plotted on a plane. The number of straight lines obtained by joining these points if no three points are collinear are

There are 12 distinct points A, B, C, ..., L, ... in order, on a circle. Lines are drawn passing through each pair of points. The total number of lines are

If in a regular polygon, the number of diagonals are 54, then the number of sides of the polygon are

The number of ways that 8 beads of different colours can be strung to form a necklace is

The number of cubic equations that can be formed with the coefficients $0,3,2,4,5,6$ when repetition of coefficients is allowed, is....

Eight chairs are numbered 1 to 8 . Two women and three men wish to occupy one chair each. First the women choose chairs from amongst the chairs marked 1 to 4 , and then the men select the chairs from amongst the remaining. The number of possible arrangements is

Five persons entered the lift cabin on the ground floor of an 8 -floor house. Suppose each of them can leave the cabin independently at any floor beginning with the first. The total number of ways in which each of the five persons can leave the cabin at any one of the 7-floor is