Formulas For Arrangements

Arrangements Formulas :

In arrangements questions, we have to arrange a group of persons fulfilling certain conditions. This is also written as sitting arrangement or sitting arrangement reasoning at some places.
 
Here we can classify these problems into 4 types:
 

Type 1. Linear Arrangement:

Here the arrangement of the persons is linear i.e. you have to arrange them in a line. Here generally a single row of arrangement is formed.

Type 2. Double row arrangement:

In these questions, there will be two groups of persons. You have to arrange one group in one row and the other group in other row. The persons in these rows normally face each other.

Type 3. Circular arrangement:

In the circular seating arrangement questions, you have to arrange the persons around a circular table etc. fulfilling certain conditions.

Type 4. Rectangular arrangement:

These arrangements are almost similar to the circular arrangements; the only difference is that the persons are sitting around a rectangular table.

Formulas for Arrangements

Read the given information carefully and answer the questions that follow.
 
Eleven friends M, N, O, P, Q, R, S, T, U, V and W are sitting in the first row of the stadium watching a cricket match.
  1. T is to the immediate left of P and third to the right of U.
  2. V is the immediate neighbour of M and N and third to the left of S.
  3. M is the second to the right of Q, who is at one of the ends.
  4. R is sitting next to the right of P and P is second to the right of O.

Question 1.

Who is sitting in the center of the row?

(A) N
(B) O
(C) S
(D) U

Solution: Option D

The arrangement of the persons is
Q W M V N U S O T P R
U is sitting in the center of the row.

Question 2.

Which of the following people are sitting to the right of S?

(A) OTPQ
(B) OTPR
(C) UNVM
(D) UOTPR

Solution: Option B

The arrangement of the persons is

Q W M V N U S O T P R
OTPR are sitting to the right of S.

Question 3.

Which of the following statements is true with respect to the above arrangement?

1. There are three persons sitting between P and S
2. W is between M and V.
3. N is sitting between V and U
4. S and O are neighbours sitting to the immediate right of T
 
(A) 1
(B) 2
(C) 3
(D) 4

Solution: Option C

The arrangement of the persons is
Q W M V N U S O T P R
Hence N is sitting between V and U.
 
Formulas for Arrangements