Advertisements
Advertisements
प्रश्न
How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
Advertisements
उत्तर
There are 4 vowels and 4 consonants in the word INVOLUTE.
Out of these, 3 vowels and 2 consonants can be chosen in \[\left( {}^4 C_3 \times^4 C_2 \right)\] ways.
The 5 letters that have been selected can be arranged in 5! ways.
∴ Required number of words =\[\left( {}^4 C_3 \times {}^4 C_2 \right) \times 5! = 4 \times 6 \times 120 = 2880\]
APPEARS IN
संबंधित प्रश्न
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:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
If P (n, 5) = 20. P(n, 3), find n ?
If nP4 = 360, find the value of 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?
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 numbers can be formed by using the digits 1 to 9 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?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels never come together?
How many words can be formed out of the letters of the word, 'ORIENTAL', so that the vowels always occupy the odd places?
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 all letters are used at a time.
How many three letter words can be made using the letters of the word 'ORIENTAL'?
Find the number of words formed by permuting all the letters of the following words:
PAKISTAN
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
How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?
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?
A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.
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 ?
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'?
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1
If 35Cn +7 = 35C4n − 2 , then write the values of n.
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 value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]
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.
Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.
Write the total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.
