हिंदी

In how many ways can 5 children be arranged in a line such that two particular children of them are always together

Advertisements
Advertisements

प्रश्न

In how many ways can 5 children be arranged in a line such that two particular children of them are always together 

योग
Advertisements

उत्तर

We consider the arrangements by taking 2 particular children together as one and hence the remaining 4 can be arranged in 4! = 24 ways.

Again two particular children taken together can be arranged in two ways.

Therefore, there are 24 × 2 = 48 total ways of arrangement.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Permutations and Combinations - Solved Examples [पृष्ठ ११७]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
अध्याय 7 Permutations and Combinations
Solved Examples | Q 4.(i) | पृष्ठ ११७

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Evaluate 8!


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 n if n – 1P3 : nP4 = 1 : 9


Find r if `""^5P_r = 2^6 P_(r-1)`


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 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?


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?


Evaluate each of the following:

8P3


Evaluate each of the following:

10P

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


The number of words from the letters of the word 'BHARAT' in which B and H will never come together, 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


Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is


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


How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?


How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?


  1. In how many ways can 8 identical beads be strung on a necklace?
  2. In how many ways can 8 boys form a ring?

Find the rank of the word ‘CHAT’ in the dictionary.


Evaluate the following.

`(3! + 1!)/(2^2!)`


The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:


If `""^(("n"  – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n


If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r


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 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


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?


How many words can be formed with the letters of the word MANAGEMENT by rearranging them?


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


In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are 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 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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×