$m$ 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
$\frac{{m\;!\;(m + 1)\;!}}{{(m - n + 1)\;!}}$
$\frac{{m\;!\;(m - 1)\;!}}{{(m - n + 1)\;!}}$
$\frac{{(m - 1)\;!\;(m + 1)\;!}}{{(m - n + 1)\;!}}$
None of these
In an election there are $5$ candidates and three vacancies. A voter can vote maximum to three candidates, then in how many ways can he vote
A committee of $4$ persons is to be formed from $2$ ladies, $2$ old men and $4$ young men such that it includes at least $1$ lady, at least $1$ old man and at most $2$ young men. Then the total number of ways in which this committee can be formed is
A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least one boy and one girl ?
Words of length $10$ are formed using the letters, $A, B, C, D, E, F, G, H, I, J$. Let $x$ be the number of such words where no letter is repeated ; and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, $\frac{y}{9 x}=$
Two packs of $52$ cards are shuffled together. The number of ways in which a man can be dealt $26$ cards so that he does not get two cards of the same suit and same denomination is