Let $x$ denote the number of ways of arranging $m$ boys and $m$ girls in a row so that no two boys sit together. If $y$ and $z$ denote the number of ways of arranging $m$ boys and $m$ girls in a row and around a circular table respectively so that boys and girls sit alternately,then $x: y: z=$
- A$m+1: m: m-1$
- B$3: 2: 1$
- C$m-1: m: 2$
- D$(m+1)m: 2m: 1$
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Similar Questions
Consider the following statements:
$I$. The number of positive integral solutions of $x_1+x_2+x_3+x_4=10$ is $286$.
$II$. If $25! = 10^n \times k, (k \in N)$, then $n=6$.
Which one of the following options is true?
$I$. The number of positive integral solutions of $x_1+x_2+x_3+x_4=10$ is $286$.
$II$. If $25! = 10^n \times k, (k \in N)$, then $n=6$.
Which one of the following options is true?
$A$ string of letters is to be formed by using $4$ letters from all the letters of the word "$MATHEMATICS$". The number of ways this can be done such that two letters are of the same kind and the other two are of a different kind is:
The word $UNIVERSITY$ is arranged randomly. The probability that both $I$s do not come together is:
Medium
View SolutionThe number of positive integral solutions of the equation $xyz = 90$ is equal to :-
The number of times the digit $3$ will be written when listing the integers from $1$ to $1000$ is
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