2. From 12 mathematicians and 9 physicists, a committee of 8 is to be formed including two physicists. The committee can consist of 2 physicists and 6 mathematicians. In how many ways can the committee be chosen so as to give a majority to mathematicians?

3. 20 persons were invited for a party. In how many ways can they and the host be seated at a circular table? In how many of these ways will two particular persons be seated on either side of the host?

4. m men and n women are to be seated in a row so that no two women sit together. If m>n, show that the number of ways in which they can be seated is

[m!(m+1)!]/(m-n+1)!.

5. Find the number of diagonals which can be obtained by joining the vertices of a polygon of n sides. How many triangles can be formed by joining the vertices of the polygon?

6. If p parallel straight lines are intersected by q parallel straight lines, then the number of parallelograms formed is

(a) (pq)/4 (b)(p-1)(q-1)/4 (c)pq(p-1)(q-1)/4 (d) None of these.

7. If nC4=126, then the value of nP4 is

(a)2564 (b) 3024 (c) 6050 (d) None of these

8. If 2nC3:nC2=44:3, then the value of n is

(a)3 (b)5 (c)6 (d) None of these

7. If nCr-1=356, nCr=84 and nCr+1=126, then r is equal to:

(a)1 (b) 2 (c) 3 (d) None of these

8.From 6 gentlemen and 4 ladies, a committee of five can be formed in

(a)200 ways (b)252 ways (c)260 ways (d)300 ways