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
Evaluate 4! – 3!
Is 3! + 4! = 7!?
Compute `(8!)/(6! xx 2!)`
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
Find r if `""^5P_r = ""^6P_(r-1)`
Find x in each of the following:
Which of the following are true:
(2 × 3)! = 2! × 3!
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?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
In how many ways can 5 different balls be distributed among three boxes?
In how many ways can 7 letters be posted in 4 letter boxes?
Evaluate each of the following:
6P6
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
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
The number of ways to arrange the letters of the word CHEESE are
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
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
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
The total number of 9 digit number which has all different digit 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:
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
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
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
