search
Log In
Welcome to GO Mechanical, where you can ask questions and receive answers from other members of the community.
1 vote

Five persons $\text{P, Q, R, S and T}$ are sitting in a row not necessarily in the same order. $Q$ and $R$ are separated by one person, and $S$ should not be seated adjacent to $Q.$

The number of distinct seating arrangements possible is:

  1. $4$
  2. $8$
  3. $10$
  4. $16$
in Numerical Ability 1.6k points
recategorized by

1 Answer

1 vote
 
Best answer

Given that, five persons $\text{P, Q, R, S, and T}$ are sitting in a row.

  1. $Q$ and $R$ are separated by one person.
  2. $S$ should not be seated adjacent to $Q.$

We can follow the above two conditions, we get the following sitting orders:

  • First fix the position of $Q,$ and $R,$ we get,
    • ${\color{Red}{Q} } \;{\color{Green}{P} }\; {\color{Blue}{R} }\; S\; T$
    • ${\color{Red}{Q} }\; {\color{Green}{P} }\; {\color{Blue}{R} }\; T\; S$
    • ${\color{Red}{Q} }\; {\color{Green}{T} }\; {\color{Blue}{R} }\; S\; P$
    • ${\color{Red}{Q} }\; {\color{Green}{T} }\; {\color{Blue}{R} }\; P\; S$
  • Again fix the position of $Q,$ and $R,$ we get,
    • $ {\color{Green}{P} }\;{\color{Red}{Q} }\; T \;{\color{Blue}{R} }\; S$
    • $ {\color{Green}{T} }\;{\color{Red}{Q} }\; P \;{\color{Blue}{R} }\; S$
  • Again fix the position of $Q,$ and $R,$ we get,
    • ${\color{Green}{S} }\; P\; {\color{Red}{Q} }\;T\;{\color{Blue}{R} }$
    • ${\color{Green}{S} }\; T\; {\color{Red}{Q} }\;P\;{\color{Blue}{R} }$

Now, we can fix the positions interchangeably, and get the following siting orders:

  • First fix the position of $R,$ and $Q,$ we get,
    • $ {\color{Blue}{R} }\; {\color{Green}{P} }\; {\color{Red}{Q} }\; T\; S$
    • ${\color{Blue}{R} }\; {\color{Green}{T} }\; {\color{Red}{Q} }\; P\; S$
  • Again fix the position of $R,$ and $Q,$ we get,
    • ${\color{Green}{S}}\;  {\color{Blue}{R} }\; P\; {\color{Red}{Q} }\; T$
    • ${\color{Green}{S}}\;  {\color{Blue}{R} }\; T\; {\color{Red}{Q} }\; P$
  • Again fix the position of $R,$ and $Q,$ we get,
    • ${\color{Green}{S}}\; P\; {\color{Blue}{R} }\; T\; {\color{Red}{Q} }$
    • ${\color{Green}{S}}\; T\; {\color{Blue}{R} }\; P\; {\color{Red}{Q} }$
    • $P\;{\color{Green}{S}}\; {\color{Blue}{R} }\; T\; {\color{Red}{Q} }$
    • $T\;{\color{Green}{S}}\; {\color{Blue}{R} }\; P\; {\color{Red}{Q} }$

$\therefore$ The number of distinct seating arrangements possible $ = 16.$

So, the correct answer is $(D).$

5.7k points 3 6 14
selected by
Answer:

Related questions

1 vote
1 answer
Five persons $\text{P, Q, R, S}$ and $\text{T}$ are to be seated in a row, all facing the same direction, but not necessarily in the same order. $\text{P}$ and $\text{T}$ cannot be seated at either end of the row. $\text{P}$ should not be seated adjacent ... is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is: $2$ $3$ $4$ $5$
asked Mar 1 in Numerical Ability jothee 4.9k points
1 vote
1 answer
In the above figure, $\textsf{O}$ is the center of the circle and, $\textsf{M}$ and $\textsf{N}$ lie on the circle. The area of the right triangle $\textsf{MON}$ is $50\;\text{cm}^{2}$. What is the area of the circle in $\text{cm}^{2}?$ $2\pi$ $50\pi$ $75\pi$ $100\pi$
asked Feb 22 in Numerical Ability gatecse 1.6k points
1 vote
1 answer
The number of hens, ducks and goats in farm $P$ are $65,91$ and $169,$ respectively. The total number of hens, ducks and goats in a nearby farm $Q$ is $416.$ The ratio of hens : ducks : goats in farm $Q$ is $5:14:13.$ All the hens, ducks and goats are sent from farm $Q$ to farm $P.$ The new ratio of hens : ducks : goats in farm $P$ is ________ $5:7:13$ $5:14:13$ $10:21:26$ $21:10:26$
asked Feb 22 in Numerical Ability gatecse 1.6k points
1 vote
1 answer
$\begin{array}{|c|c|} \hline \textbf{Company} & \textbf{Ratio} \\\hline C1 & 3:2 \\\hline C2 & 1:4 \\\hline C3 & 5:3 \\\hline C4 & 2:3 \\\hline C5 & 9:1 \\\hline C6 & 3:4 \\\hline\end{array}$ The distribution of employees at the rank ... $\textsf{C2}$ and $\textsf{C5}$ together is ________. $225$ $600$ $1900$ $2500$
asked Feb 22 in Numerical Ability gatecse 1.6k points
1 vote
1 answer
The bar graph shows the data of the students who appeared and passed in an examination for four schools $P, Q, R$, and $S$. The average of success rates $\text{(in percentage)}$ of these four schools is _______. $58.5\%$ $58.8\%$ $59.0\%$ $59.3\%$
asked Feb 19, 2020 in Numerical Ability jothee 4.9k points
...