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 ______.
पर्याय
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
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
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?
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
Which of the following are true:
(2 × 3)! = 2! × 3!
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
Evaluate each of the following:
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?
The number of five-digit telephone numbers having at least one of their digits repeated is
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
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
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 can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
Evaluate the following.
`((3!)! xx 2!)/(5!)`
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 ______.
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
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. In how many arrangements will all 6 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?
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never 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
GARDEN
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?
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
The total number of 9 digit numbers which have all different digits is ______.
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.
