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 .

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 .

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

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)!)

If m red balls and n white balls are placed in a row so that no two white balls are together, prove that if m gt n , the total number of ways in which this can be done is ""^(m+1)C_(n) .

If m red balls and n white balls are placed in a row so that no two white balls are together, prove that if m > n, the total number of ways in which this can be done is ""^(m+1)C_(n) .

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: 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