The number of ways in which $5$ persons $P, Q, R, S$ and $T$ can be seated in a ring so that $P$ sits between $Q$ and $R$ is

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Solution

We either have $Q P R$ or $R P Q$ . In each of these cases remaining
two persons will set in $2$ ways.
$\Rightarrow$ There are four ways.

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Study the following information to answer the given questions:
Twelve people are sitting in two parallel rows containing six people each, in such a way that there is an equal distance between adjacent persons. In row 1, P, Q, R, S, T and V are seated and all of them are facing south. In row 2, A, B, C, D, E and F are seated and all of them are facing north. Therefore, in the given seating arrangement each member seated in a row faces another member of the other row.
S sits third to the right of Q. Either S or Q sits at an extreme end of the line. The one who faces Q sits second to the right of E. Two people sit between B and F. Neither B nor F sits at an extreme end of the line. The immediate neighbour of B faces the person who sits third to the left of P. R and T are immediate neighbours of each other. C sits second to the left of A. T does not face the immediate neighbour of D.
How many persons are seated between V and R ?

Q. Study the following information carefully and answer the given questions.
P, Q, R, S, T, V, X and Y are seated in a straight line facing north. P sits fourth to the left of V. V sits either sixth from the left end of the line or fourth from the right end of the line. S sits second to the right of R. R is not an immediate neighbour of V. T and Q are immediate neighbours of each other but neither T nor Q sits at extreme ends of the line. Only one person sits between T and X. X does not sit at the extreme end of the line.
Which of the following represents persons seated at the two extreme ends of the line?

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The number of ways in which 5 persons P,Q,R,S and T can be seated in a ring so that P sits between Q and R is

We either have QPR or RPQ. In each of these cases remainingtwo persons will set in 2 ways.⇒ There are four ways.

The number of ways in which $5$ persons $P, Q, R, S$ and $T$ can be seated in a ring so that $P$ sits between $Q$ and $R$ is

We either have $Q P R$ or $R P Q$ . In each of these cases remaining
two persons will set in $2$ ways.
$\Rightarrow$ There are four ways.