If alpha represents the number of arrangement | vedclass

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(B) For linear arrangement,treat $p$ men as one unit. There are $q$ women and $1$ unit of men,totaling $q+1$ items. These can be arranged in $(q+1)!$

Vedclass · Accepted Answer

$(q+1): 1$

Vedclass · Answer

(B) For linear arrangement,treat $p$ men as one unit. There are $q$ women and $1$ unit of men,totaling $q+1$ items. These can be arranged in $(q+1)!$ ways. The $p$ men can be arranged among themselves in $p!$ ways. So,$\alpha = p!(q+1)!$.For circular arrangement,treat $p$ men as one unit. There are $q$ women and $1$ unit of men,totaling $q+1$ items. These can be arranged in a circle in $(q+1-1)! = q!$ ways. The $p$ men can be arranged among themselves in $p!$ ways. So,$\beta = p!q!$.Therefore,$\frac{\alpha}{\beta} = \frac{p!(q+1)!}{p!q!} = \frac{(q+1) 	imes q!}{q!} = q+1$.Thus,$\alpha : \beta = (q+1) : 1$.

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

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