Advertisements
Advertisements
प्रश्न
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels occupy only the odd places?
Advertisements
उत्तर
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
संबंधित प्रश्न
Convert the following products into factorials:
5 · 6 · 7 · 8 · 9 · 10
If (n + 2)! = 60 [(n − 1)!], find n.
If P (5, r) = P (6, r − 1), find r ?
If P (n, 5) = 20. P(n, 3), find n ?
If nP4 = 360, find the value of n.
If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?
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?
In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?
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 'STRANGE' be arranged so that
the vowels never come together?
How many different words can be formed with the letters of word 'SUNDAY'? How many of the words begin with N? How many begin with N and end in Y?
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 different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels are always together?
How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:
the vowels always occupy even places?
How many permutations can be formed by the letters of the word, 'VOWELS', when
all consonants come together?
Find the number of words formed by permuting all the letters of the following words:
INDEPENDENCE
Find the number of words formed by permuting all the letters of the following words:
ARRANGE
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
Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.
How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?
How many different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?
How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.
How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?
There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?
Find the total number of permutations of the letters of the word 'INSTITUTE'.
The letters of the word 'ZENITH' are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word 'ZENITH'?
Evaluate
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
nCr + 2 · nCr − 1 + nCr − 2 = n + 2Cr.
How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if (i) 4 letters are used at a time
How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
Write the number of diagonals of an n-sided polygon.
Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.
