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

Q56 / 160 · TS EAMCET 2020 (11 Sep Shift 2) · Mathematics

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

A
$(q+1) p !: 1$
Correct answer
B
$(q+1): 1$
C
$1: p !$
D
$p$ ! :q!

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 $=p ! q !$ $\Rightarrow \quad \frac{\alpha}{\beta}=\frac{p !(q+1) !}{p ! q \mid !}=(q+1): 1$

Hence, the correct answer is option: 'B'.

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