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#1 2007-10-07 02:26:07

ganesh
Registered: 2005-06-28
Posts: 25,867

Permutations and Combinations Vol.I

1. Find the total number of 9 digit numbers which have all different digits.

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

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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