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m men and n women are to be seated in a row so that no two wom

Question

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

\frac{( m + 1 )! m !}{( m + n + 1 )!}

\frac{( m + 1 )! m !}{( m + n - 1 )!}

\frac{( m - 1 )! m !}{( m - n + 1 )!}

\frac{( m + 1 )! m !}{( m - n + 1 )!}

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Isabella Discussed

m

men and

n

women are to be seated in a row so that no two women sit together. If

m > n

, then show that the number of ways in which they can be seated is,

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

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_{m}

ways.
Therefore, total number of ways is

= m! \times^{m + 1} P_{n} = m! \times \frac{( m + 1 )!}{( m + 1 - n )!} = \frac{( m + 1 )! m !}{( m - n + 1 )!}

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Question Text	$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$ , then show that the number of ways in which they can be seated is,
Answer Type	Text solution:1
Upvotes	150