Advertisements
Advertisements
Question
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels occupy only the odd places?
Advertisements
Solution
There are 7 letters in the word STRANGE.
We wish to find the total number of arrangements of these 7 letters so that the vowels occupy only odd positions.
There are 2 vowels and 4 odd positions.
These 2 vowels can be arranged in the 4 positions in 4\[\times\]3 ways, i.e. 12 ways.The remaining 5 consonants can be arranged in the remaining 5 positions in 5! ways.
By fundamental principle of counting:
Total number of arrangements = 12\[\times\]5! = 1440
APPEARS IN
RELATED QUESTIONS
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
If (n + 2)! = 60 [(n − 1)!], find n.
Prove that:
If P (9, r) = 3024, find r.
If P(11, r) = P (12, r − 1) find r.
If P (n, 4) = 12 . P (n, 2), find n.
If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.
Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?
Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
How many 6-digit telephone numbers can be constructed with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?
How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?
In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?
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 can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?
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?
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 all letters are used at a time.
Find the number of words formed by permuting all the letters of the following words:
INTERMEDIATE
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:
EXERCISES
Find the number of words formed by permuting all the letters of the following words:
CONSTANTINOPLE
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.
Find the total number of permutations of the letters of the word 'INSTITUTE'.
Find the total number of ways in which six ‘+’ and four ‘−’ signs can be arranged in a line such that no two ‘−’ signs occur together.
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
Evaluate
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 diagonals of an n-sided polygon.
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.
Write the number of ways in which 5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.
