The first ten English alphabets are written on slips of paper and placed in a box Three of the slips re drawn and placed in order. How many arrangements are possible?

The digits, from 0 to 9 are written on 10 slips of paper (one digit on each slip) and placed in a box. If three of the slips are drawn and arranged, then the number of possible different arrangements is

It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible ?

It is required to seat 8 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

It is required to sent 7 men and 3 women in a row so that women occupy the even places. How many such arrangements are possible?

Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from twenty six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?

When a group photograph is taken, all the seven teachers should be in the first row and all the twenty students should be in the second row. If the two corners of the second row are reserved for the two tallest students, interchangeable only between them, and if the middle seat of the front row is reserved for the Principal, how many arrangements are possible?

In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 at the back? How many seating arrangements are possible if 3 girls sit together in a back row on adjacent seats?

In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 at the back? How many seating arrangements are possible if 3 girls sit together in a back row on adjacent seats?Now, if all the seating arrangements are equally likely, what is the probability of 3 girls sitting together in a back row on adjacent seats?

There are ten points in the plane, no three of which are coolinear. How many different lines can be drawn through these points ?

In how many ways, can three girls can three girls and nine boys be seated in two vans, each having numbered seats, 3 in the and 4 at the back? How many seating arrangements are possible if 3 girls should sit together in a back row on adjacent seats? Now, if all the seating arrangements are equally likely, what is the probability of 3 girls sitting together in a back row on adjacent seats?