Advertisements
Advertisements
Question
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
Options
576
4C3 × 4!
2 × 4!
none of these.
Advertisements
Solution
576
There are 3 even places in the 7 letter word ARTICLE.
So, we have to arrange 4 consonants in these 3 places in 4P3 ways.
And the remaining 4 letters can be arranged among themselves in 4! ways.
∴ Total number of ways of arrangement = 4P3 x 4! = 4! x 4! = 576
APPEARS IN
RELATED QUESTIONS
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 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
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.
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
Evaluate each of the following:
P(6, 4)
In how many ways can 4 letters be posted in 5 letter boxes?
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
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 all possible words that can be formed using the letters of the word 'MATHEMATICS'.
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
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
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
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 ways can the product a2 b3 c4 be expressed without exponents?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
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 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
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?
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
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.
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?
A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is ______.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
