Advertisements
Advertisements
प्रश्न
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
विकल्प
1440
144
7!
4C4 × 3C3
Advertisements
उत्तर
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is 144.
Explanation:
Total number of letters in the ‘ARTICLE’ is 7 out which A, E, I are vowels and R, T, C, L are consonants
Given that vowels occupy even place
∴ Possible arrangement can be shown as below
C, V, C, V, C, V, C i.e. on 2nd, 4th and 6th places
Therefore, number of arrangement = 3P3 = 3! = 6 ways
Now consonants can be placed at 1, 3, 5 and 7th place
∴ Number of arrangement = 4P4 = 4! = 24
So, the total number of arrangements = 6 × 24 = 144.
APPEARS IN
संबंधित प्रश्न
Evaluate 8!
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?
Find r if `""^5P_r = 2^6 P_(r-1)`
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
In how many ways can 7 letters be posted in 4 letter boxes?
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
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
Write the number of arrangements of the letters of the word BANANA in which two N's come 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
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, 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
Find x if `1/(6!) + 1/(7!) = x/(8!)`
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
Find the rank of the word ‘CHAT’ in the dictionary.
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?
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
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 divisible by 4?
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
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
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.
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! |
