' m ' men and ' n ' women are to be seated in a row so that no two women sit together. If m n , then the number of ways in which they can be seated is ( m − n + 1 )! m ! ( m + 1

Question

' m ' men and ' n ' women are to be seated in a row so that no two women sit together. If m > n , then the number of ways in which they can be seated is ( m − n + 1 )! m ! ( m + 1 )! × λ ​ . Then the value of ' λ ' is

TestHub · Accepted Answer

' m ' men can be seated in m ! ways creating ( m + 1 ) for ladies to sit. ​ ′ n ’ladies out of ( m + 1 ) places (as n < m ) can be seated in m + 1 P n ​ ways ​ ​ ​ = m ! × m + 1 P n ​ = m ! ( m + 1 − n )! ( m + 1 )! ​ ∴ T o t a lw a ys

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