English

In How Many Ways Can the Letters of the Word 'Failure' Be Arranged So that the Consonants May Occupy Only Odd Positions?

Advertisements
Advertisements

Question

In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?

Advertisements

Solution

There are 7 letters in the word FAILURE.
We wish to find the total number of arrangements of these 7 letters so that the consonants occupy only odd positions.
There are 3 consonants and 4 odd positions. These 3 consonants can be arranged in the 4 positions in 4! ways.
Now, the remaining 4 vowels can be arranged in the remaining 4 positions in 4! ways.

By fundamental principle of counting:
Total number of arrangements = 4! \[\times\] 4! = 576

shaalaa.com
Factorial N (N!) Permutations and Combinations
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.4 [Page 36]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.4 | Q 1 | Page 36

RELATED QUESTIONS

Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18


Convert the following products into factorials: 

(n + 1) (n + 2) (n + 3) ... (2n)


Prove that: n! (n + 2) = n! + (n + 1)!


If (n + 1)! = 90 [(n − 1)!], find n.


If (n + 3)! = 56 [(n + 1)!], find n.


If \[\frac{(2n)!}{3! (2n - 3)!}\]  and \[\frac{n!}{2! (n - 2)!}\]  are in the ratio 44 : 3, find n.

 

 


Prove that:

\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]


If 5 P(4, n) = 6. P (5, n − 1), find n ?


If nP4 = 360, find the value of n.


If P(11, r) = P (12, r − 1) find r.


If P (n, 4) = 12 . P (n, 2), find n.


Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?


How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?


There are two works each of 3 volumes and two works each of 2 volumes; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?


If a denotes the number of permutations of (x + 2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of  permutations of x − 11 things taken all at a time such that a = 182 bc, find the value of x.


How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits 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?


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels come together?

 


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels never come together? 


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels occupy only the odd places?


How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the letters P and I respectively occupy first and last place?


How many permutations can be formed by the letters of the word, 'VOWELS', when

there is no restriction on letters?


How many permutations can be formed by the letters of the word, 'VOWELS', when

each word begins with O and ends with L?


How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if 4 letters are used at a time?


Find the number of words formed by permuting all the letters of the following words:

INDIA


Find the number of words formed by permuting all the letters of the following words:

PAKISTAN


In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?


Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.


There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?


How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?


In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?


Find the total number of permutations of the letters of the word 'INSTITUTE'.


If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?


In how many ways can the letters of the word "INTERMEDIATE" be arranged so that:

the relative order of vowels and consonants do not alter?


For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1 


There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
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.


Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×