Advertisements
Advertisements
प्रश्न
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
Advertisements
उत्तर
There should be 4 letters between P and S.
Suppose the places of 12 letters have been named 1, 2, 3,... 12.
1 2 3 4 5 6 7 8 9 10 11 12
Thus, P can be placed at positions 1, 2, 3, 4, 5, 6, 7 and S can be placed at positions 6, 7, 8, 9, 10, 11, 12.
⇒ P and S can be placed at 7 places.
Similarly, S and P can be placed in 7 places.
P and S or S and P can be arranged in 7 + 7 = 14 ways.
The remaining 10 letters can be arranged in `(10!)/(2!)` ways.
∴ Number of words when there are 4 letters between P and S = `(10!)/(2!) xx 14 = 10! xx 7`
= 25401600.
APPEARS IN
संबंधित प्रश्न
Compute `(8!)/(6! xx 2!)`
if `1/(6!) + 1/(7!) = x/(8!)`, find x
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 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?
Find the number of ways in which one can post 5 letters in 7 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?
Evaluate each of the following:
Evaluate each of the following:
P(6, 4)
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
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
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
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
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 numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The number of ways to arrange the letters of the word “CHEESE”:
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
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 distinct permutations of the letters of the word MISSISSIPPI?
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?
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 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?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
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.
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.
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 ______.
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
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 |
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
