Advertisements
Advertisements
Question
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
Options
60 × 5!
15 × 4! × 5!
4! × 5!
none of these.
Solution
60 × 5!
The four people, i.e A, B and the two persons between them are always together. Thus, they can be considered as a single person.
So, along with the remaining 4 persons, there are now total 5 people who need to be arranged. This can be done in 5! ways.
But, the two persons that have to be included between A and B could be selected out of the remaining 6 people in 6P2 ways, which is equal to 30.
For each selection, these two persons standing between A and B can be arranged among themselves in 2 ways.
∴ Total number of arrangements = 5! x 30 x 2 = 60 x 5!
APPEARS IN
RELATED QUESTIONS
Find r if `""^5P_r = 2^6 P_(r-1)`
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?
How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
In how many ways can 5 different balls be distributed among three boxes?
Evaluate each of the following:
8P3
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
The number of permutation of n different things taken r at a time, when the repetition is allowed is:
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The total number of 9 digit numbers which have all different digits is ______.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
