1. Tardigrade
  2. Question
  3. Mathematics
  4. If α represents the number of arrangements of p men and q women in a row such that all men are together and β represents the number of circular arrangements of the same people with the same condition, then α: β is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $\alpha$ represents the number of arrangements of $p$ men and $q$ women in a row such that all men are together and $\beta$ represents the number of circular arrangements of the same people with the same condition, then $\alpha: \beta$ is

TS EAMCET 2020

Solution:

Given all men are together
$\therefore $ Linear arrangement of $p$ men and $q$ women $=p !(q+1) !$
and circular arrangement of $p$ men and $q$ women $=p ! q !$
$\Rightarrow \frac{\alpha}{\beta}=\frac{p !(q+1) !}{p ! q \mid !}=(q+1): 1$