Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
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!
= 6 × 6 × 2
= 72
APPEARS IN
संबंधित प्रश्न
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 = 2^6 P_(r-1)`
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?
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
Find x in each of the following:
Find x in each of the following:
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
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:
Evaluate each of the following:
6P6
In how many ways can 4 letters be posted in 5 letter boxes?
The number of five-digit telephone numbers having at least one of their digits repeated is
The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
The total number of 9 digit number which has all different digit is:
The number of ways to arrange the letters of the word “CHEESE”:
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
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?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
