हिंदी

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, 576 , 4c3 × 4!, 2 × 4! , None of These.

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • 576

  • 4C3 × 4!

  • 2 × 4!

  • none of these.

MCQ
Advertisements

उत्तर

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  = 4Px 4! = 4! x 4! = 576

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.7 [पृष्ठ ४७]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.7 | Q 21 | पृष्ठ ४७

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Evaluate 8!


if `1/(6!) + 1/(7!) = x/(8!)`, find x


Find n if n – 1P3 : nP4 = 1 : 9


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.


In how many ways can three jobs I, II and III be assigned to three persons AB and C if one person is assigned only one job and all are capable of doing each job?


How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?


Find the number of ways in which one can post 5 letters in 7 letter boxes ?


In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?


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 ?


In how many ways can 4 letters be posted in 5 letter boxes?


Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?


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 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?


Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?


How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?


The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters 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


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?


The total number of 9 digit number which has all different digit is:


Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?


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?


A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?


Find the distinct permutations of the letters of the word MISSISSIPPI?


A coin is tossed 8 times, how many different sequences of heads and tails are possible?


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?


Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?


In how many ways can 5 children be arranged in a line such that two particular children of them are always together 


In how many ways can 5 children be arranged in a line such that two particular children of them are never together.


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.


Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`


The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.


Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.


Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are 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?


The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.


If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×