The number of ways of arranging `m` positive and `n(lt m+1)` negative signs in a row so that no two are together is a.= `^m+1p_n` b.=`^n+1p_m`= c.=`^m+1c_n`="" d.=`^n+1c_m`

Show that the number of ways in which p positive and n negative signs may be placed in a row so that no two negative signs shall be together is (p+1)C_n .

The number of ways in which m+n(nlem+1) different things can be arranged in a row such that no two of the n things may be together, is

The number of ways in which m men and n women can be seated in a row, so that no two women sit together is (i) (m!(m+1)!)/((m+n-1)!) (ii) (m!(m+1)!)/((m-n+1)!) (iii) (n!(m+1)!)/((m-n+1)!) (iv) (m!(n+1)!)/((m+n-1)!)

Number iof ways in which m men and n women can be arranged in a rwo so that no two women are together is m!^(m=1)P_n Also number oif ways in which m men and n women can be seated in a row so that all the n women are together is (m=1)!n! On the basis of above informatiion answer the following question: Number of ways in which 10 boys and 5 girls can be seated in a row so that no boy sits between girls is (A) 5!xx10_P_5 (B) 5!xx11_P_5 (C) 10!xx11_P_5 (D) 5!xx11

Number iof ways in which m men and n women can be arranged in a rwo so that no two women are together is m!^(m=1)P_n Also number oif ways in which m men and n women can be seated in a row so that all the n women are together is (m=1)!n! On the basis of above informatiion answer the following question the no of ways in which 10 boys & 5 girls: seated in row so that no boy sits between girls

Number iof ways in which m men and n women can be arranged in a rwo so that no two women are together is m!^(m=1)P_n Also number oif ways in which m men and n women can be seated in a row so that all the n women are together is (m=1)!n! On the basis of above informatiion answer the following question: Therre are 10 intermediate stations between two places P and Q. the number of ways in 10 boys &5 girls can be seated in a row so that no boy sits between girls

2m white counters and 2n red counters are arranged in a straight line with (m+n) counters on each side of central mark. The number of ways of arranging the counters, so that the arrangements are symmetrical with respect to the central mark is (A) .^(m+n)C_m (B) .^(2m+2n)C_(2m) (C) 1/2 ((m+n)!)/(m! n!) (D) None of these

If the sum of m terms of an A.P. is the same as the sum of its n terms, then the sum of its (m+n) terms is (a). m n (b). -m n (c). 1//m n (d). 0

Straight lines are drawn by joining m points on a straight line of n points on another line. Then excluding the given points, the number of point of intersections of the lines drawn is (no tow lines drawn are parallel and no these lines are concurrent). a. 4m n(m-1)(n-1) b. 1/2m n(m-1)(n-1) c. 1/2m^2n^2 d. 1/4m^2n^2

If the m^(t h) term of an A.P. is 1/n and the n^(t h) terms is 1/m , show that the sum of m n terms is 1/2(m n+1)dot