Advertisements
Advertisements
प्रश्न
How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?
Advertisements
उत्तर
The word PARALLEL consists of 8 letters that include two As and three Ls.
Total number of words that can be formed using the letters of the word PARALLEL =\[\frac{8!}{2!3!}\] = 3360
Number of words in which all the Ls come together is equal to the condition if all three Ls are considered as a single entity.
So, we are left with total 6 letters that can be arranged in\[\frac{6!}{2!}\] ways (divided by 2! since there are two As), which is equal to 360.Number of words in which all Ls do not come together = Total number of words\[-\] Number of words in which all the Ls come together = 3360\[-\]360= 3000
APPEARS IN
संबंधित प्रश्न
Convert the following products into factorials:
5 · 6 · 7 · 8 · 9 · 10
Convert the following products into factorials:
3 · 6 · 9 · 12 · 15 · 18
Prove that:
If P (9, r) = 3024, find r.
If P (n − 1, 3) : P (n, 4) = 1 : 9, find 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.
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?
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 letter G always occupies the first place?
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 always occupy even places?
How many permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with E?
m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]
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
Find the number of words formed by permuting all the letters of the following words:
RUSSIA
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 by arranging the letters of the word 'MUMBAI' so that all M's come together?
How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.
How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?
Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.
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 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?
If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.
For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1
Evaluate
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · n − 1Cr − 1 = (n − r + 1) nCr − 1
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
If 35Cn +7 = 35C4n − 2 , then write the values of n.
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.
