मराठी

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 ? - Mathematics

Advertisements
Advertisements

प्रश्न

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 ?

Advertisements

उत्तर


Each of the seven men can be arranged amongst themselves in 7! ways.
The women can be arranged amongst themselves in seven places, in 6! ways (i.e. nthings can be arranged in (n-1)! ways around a round table).
By fundamental principle of counting, total number of ways = 7! x 6!

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.6 [पृष्ठ ४५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.6 | Q 6 | पृष्ठ ४५

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Compute `(8!)/(6! xx 2!)`


Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5


How many 4-digit numbers are there with no digit repeated?


Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?


Find r if `""^5P_r = ""^6P_(r-1)`


Which of the following are true:

(2 +3)! = 2! + 3!


Which of the following are true:

(2 × 3)! = 2! × 3!


In how many ways can 7 letters be posted in 4 letter boxes?


In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?


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 ?


Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?


In how many ways 4 women draw water from 4 taps, if no tap remains unused?


Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?


Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?


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 six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters 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


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 numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?


If nP4 = 12(nP2), find n.


In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?


The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters 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?


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 ways can the product a2 b3 c4 be expressed without exponents?


In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?


How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together


How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together


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 of these 6-digit numbers are even?


Choose the correct alternative:
The product of r consecutive positive integers is divisible b


In how many ways can 5 children be arranged in a line such that two particular children of them are never together.


A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is ______.


The total number of 9 digit numbers which have all different digits 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!

Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.


If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×