Advertisements
Advertisements
प्रश्न
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
Advertisements
उत्तर
Among the 5! = 120 permutations of 5 children.
There are 48 in which two children are together.
In the remaining 120 – 48 = 72 permutations
Two particular children are never together.
APPEARS IN
संबंधित प्रश्न
Evaluate 4! – 3!
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Find x in each of the following:
Find x in each of the following:
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
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?
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?
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 ?
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?
The number of permutations of n different things taking r at a time when 3 particular things are to be included 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
The product of r consecutive positive integers is divisible by
The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants 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
If (n+2)! = 60[(n–1)!], find n
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?
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
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 all the vowels are 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
DANGER
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
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)`
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
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 number of 5-digit telephone numbers having atleast one of their digits repeated 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! |
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
