Advertisements
Advertisements
Question
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?
Advertisements
Solution
The word GANESHPURI consists of 10 distinct letters.
Number of letters = 10!
If we fix the first letter as G, the remaining 9 letters can be arranged in 9! ways to form the words.
∴ Number of words starting with the letter G = 9!
APPEARS IN
RELATED QUESTIONS
Prove that: n! (n + 2) = n! + (n + 1)!
If (n + 1)! = 90 [(n − 1)!], find n.
Prove that:
If 5 P(4, n) = 6. P (5, n − 1), find n ?
If P (n, 4) = 12 . P (n, 2), find n.
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.
Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (n, n) = P (n + 1, n + 1) − 1.
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.
There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?
How many three-digit numbers are there, with no digit repeated?
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?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels occupy only 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?
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 all 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 but first is vowel.
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:
RUSSIA
Find the number of words formed by permuting all the letters of the following words:
EXERCISES
How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?
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?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
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'.
In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?
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:
n · n − 1Cr − 1 = (n − r + 1) nCr − 1
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
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
Write the number of diagonals of an n-sided polygon.
Write the value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]
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 total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants.
