1. If $m>n,$ the number of ways m men and n women can be seated in a row, so that no two women sit together, is

2. In a certain test $a_i$ students gave wrong answers to atleast i questions, where i=1, 2, 3, ....k. No students gave more than k wrong answers. The total number of wrong answers is

3. Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs marked 1 to 4 and then the men select from amongst the remaining chairs. The number of seating arrangements is

4. Five balls of different colours are to be placed in 3 boxes of different sizes. Each box can hold all five balls. The number of ways, we can place the balls so that no box is empty, is

5. A candidate is required to answer 6 out of 10 questions which are divided into 2 groups containing 5 questions each and he is not permitted to attempt more than 4 questions from each group. The number of ways he can make up his choice is

6. Ten different letters of an alphabet are given. Words with 5 letters are formed from the given letters. The number of words which have atleast one letter repeated is

7. Six boys and six girls sit in a row. The number of ways they can be seated when the girls are separated is

8. Six $X^s$are to be placed in the squares of the figure given below such that each row contains atleast one X.

The number of ways this can be done is

9. A host invites 20 person for a party. The nukmber of ways they can be seated at a circular table, such that two particular persons be seated on either side of the host, is

10. The number of numbers greater than 3000, which can be formed by using the digits 0,1,2,3,4,5 without repetition is

11. The number of positive integers, which can be formed by using any number of digits 0, 1, 2, 3, 4, 5 using each digit not more than once in each number, is

12. Given 5 different green dyes, 4 different blue dyes and 3 different red dyes, the number of combination of dyes taking atleast one green dye and one blue dye, is

13. The number of ways in which 5 identical balls can be kept in 10 identical boxes, if not more than one can go into a box, is

14. The number of ways in which ten candidates $A_1$, $A_2$,.....$A_{10}$ can be ranked, if $A_1$ is always above $A_2$, is

15. A round table conference is to be held among 20 delegates of 20 countries.The number of ways they can be seated, if two particular delegates are never sit together, is

16. The number of the numbers that can be formed by using all the digits from 1, 2, 3, 4, 3, 2,1, so that odd digits occupy odd places, is

17. From 6 men and 4 women the number of ways of forming a committee of 5, if there is no restriction on its formation, is

18. There are six men A, B, C, D, E, F. The number of ways of forming a committee of four so as to always include C and exclude D, is

19. The number of numbers greater than 1000, but not greater than 4000 that can be formed with the digits 0, 1, 2, 3, 4, if repetition of digits being allowed is

20. There are 3 copies each of 4 different books. The number of ways they can be arranged in a sheld is

21. The number of permutations of the letters of the word BANANA is

22. In a class of 10 students there are 3 girls. The number of ways they can be arranged in a row, so that no 2 girls are consecutive, is $k·8!$ where k=

23. A committee of 6 is chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. The number of ways this can be done, if two particular women refuse to serve on the same committee, is

24. At an election, three wards of a town are canvassed by 4, 5 and 8 men respectively. If there are 20 men volunteer, then the number of ways they can be allotted to different wards is