Advertisements
Advertisements
प्रश्न
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
Advertisements
उत्तर
In the word PERMUTATIONS, there are 2 Ts and all the other letters appear only once.
There are 5 vowels in the given word, each appearing only once.
Since they have to always occur together, they are treated as a single object for the time being. This single object together with the remaining 7 objects will account for 8 objects. These 8 objects in which there are 2 Ts can be arranged in `(8!)/(2!)` ways
Corresponding to each of these arrangements, the 5 different vowels can be arranged in 5! ways.
Therefore, by multiplication principle, required number of arrangements in this case
= `(8!)/(2!) xx 5! = (40320 xx 120)/2`
= 2419200.
APPEARS IN
संबंधित प्रश्न
Evaluate 8!
Evaluate 4! – 3!
Is 3! + 4! = 7!?
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
How many 4-digit numbers are there with no digit repeated?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
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 ?
Evaluate each of the following:
8P3
Evaluate each of the following:
6P6
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
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 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
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 words from the letters of the word 'BHARAT' in which B and H will never come together, is
The number of ways to arrange the letters of the word CHEESE are
The number of arrangements of the letters of the word BHARAT taking 3 at a time 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
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
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
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 0! + 0!)/(2!)`
Evaluate the following.
`(3! + 1!)/(2^2!)`
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?
8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
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?
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
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.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
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 |
