Advertisements
Advertisements
Question
Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.
Solution
Let us denote married couples by S1, S2, S3
Where each couple is considered to be a single unit as shown in the following figure:
Then the number of ways in which spouces can be seated next to each other is 3! = 6 ways.
Again each couple can be seated in 2! ways.
Thus the total number of seating arrangement so that spouces sit next to each other = 3! × 2! × 2! × 2! = 48.
Again, if three ladies sit together, then necessarily three men must sit together.
Thus, ladies and men can be arranged altogether among themselves in 2! ways.
Therefore, the total number of ways where ladies sit together is 3! × 3! × 2! = 144.
APPEARS IN
RELATED QUESTIONS
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
Find r if `""^5P_r = ""^6P_(r-1)`
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
In how many ways can 7 letters be posted in 4 letter boxes?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
Evaluate each of the following:
6P6
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
The product of r consecutive positive integers is divisible by
If (n+2)! = 60[(n–1)!], find n
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
Evaluate the following.
`(3! + 1!)/(2^2!)`
The possible outcomes when a coin is tossed five times:
The number of ways to arrange the letters of the word “CHEESE”:
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
What is the maximum number of different answers can the students give?
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
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many distinct 6-digit numbers are there?
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
DANGER
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
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 ______.
8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
