TS EAMCET · Maths · Permutation Combination
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 \((q+1) p !: 1\)
- B \((q+1): 1\)
- C \(1: p !\)
- D \(p\) ! :q!
Answer & Solution
Correct Answer
(B) \((q+1): 1\)
Step-by-step Solution
Detailed explanation
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 \(=p ! q !\) \(\Rightarrow \quad \frac{\alpha}{\beta}=\frac{p !(q+1) !}{p ! q \mid !}=(q+1): 1\)
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