The number of different ways in which 8 persons can stand in a row so

1.	The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is A. 60 × 5! B. 15 × 4! × 5! C. 4! × 5! D. none of these
Answer» Option : (D) As, It is required that, two particular persons A and B there are always two persons so, let us consider this arrangement be "AxxB" and consider it as a single object. So, We are left with, 4 persons and an object, i.e. total 5 objects. Now, This 5 objects can be arranged in 5! ways. Again, The two 'x' are to be filled with 2 persons from 6 persons, this can be done in ⁶P₂ = 30 ways. Two persons ‘A’ and ‘B’ can be arranged in 2! = 2 ways. So, The total number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is = 5! x 30 x 2 = 5! x 60.

The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is A. 60 × 5! B. 15 × 4! × 5! C. 4! × 5! D. none of these

Answer»

Option : (D)

As, It is required that, two particular persons A and B there are always two persons so, let us consider this arrangement be "AxxB" and consider it as a single object.

So,

We are left with, 4 persons and an object, i.e. total 5 objects.

Now,

This 5 objects can be arranged in 5! ways.

Again,

The two 'x' are to be filled with 2 persons from 6 persons, this can be done in ⁶P₂ = 30 ways.

Two persons ‘A’ and ‘B’ can be arranged in 2! = 2 ways.

So,

The total number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is = 5! x 30 x 2

= 5! x 60.

Discussion

No Comment Found

Related InterviewSolutions

A number lock on a suitcase has three wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.
A number lock on a suitcase has 3 wheels each labeled with ten digits 0 to 9. If the opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.
How many different words can be formed with the letters of the word ‘CAPTAIN’? In how many of these C and T are never together?
In how many ways can the letters of the word ‘ARRANGE’ be arranged so that the two R’s are never together?
In how many ways can the letters of the word ‘ARRANGE’ be arranged so that the two R’s are never together?
The number of words from the letters of the word ‘BHARAT’ in which B and H will never come together, is A. 360 B. 240 C. 120 D. none of these
Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.
How many words, with or without meaning, can be formed using all theletters of the word EQUATION, using each letter exactly once.
The number of ways to arrange the letters of the word CHEESE are A. 120 B. 240 C. 720 D. 6
In how many ways can the letters of the word ‘PENCIL’ be arranged so that N is always next to E?