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 4! – 3!
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
How many 4-digit numbers are there with no digit repeated?
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
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:
Which of the following are true:
(2 +3)! = 2! + 3!
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
Evaluate each of the following:
6P6
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
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 words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate 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
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
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
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?
Find the rank of the word ‘CHAT’ in the dictionary.
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
The number of ways to arrange the letters of the word “CHEESE”:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
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
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
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?
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
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 ______.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are 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.
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?
