Permutations And Combinations Ques 28
- $m$ 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
$$ \frac{m !(m+1) !}{(m-n+1) !} $$
(1983, 2M)
Show Answer
Answer:
Correct Answer: 28.$(n=9$ and $r=3)$
Solution:
Formula:
- Since $m$ men and $n$ women are to be seated in a row so that no two women sit together. This could be shown as
$$ \times M_1 \times M_2 \times M_3 \times \ldots \times M_m \times $$
which shows there are $(m+1)$ places for $n$ women.
$\therefore$ Number of ways in which they can be arranged.
$$ \begin{aligned} & =(m) !{ }^{m+1} P _n \\ & =\frac{m! \cdot (m+1)!}{(m+1-n)!} \end{aligned} $$
BETA
