Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Convert the following products into factorials:
5 · 6 · 7 · 8 · 9 · 10
Convert the following products into factorials:
1 · 3 · 5 · 7 · 9 ... (2n − 1)
If (n + 2)! = 60 [(n − 1)!], find n.
If (n + 1)! = 90 [(n − 1)!], find n.
Prove that:
Prove that:
If P (5, r) = P (6, r − 1), find r ?
If P (n, 5) = 20. P(n, 3), find n ?
If P (9, r) = 3024, find r.
Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (n, n) = P (n + 1, n + 1) − 1.
Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?
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?
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?
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.
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels come together?
How many permutations can be formed by the letters of the word, 'VOWELS', when
all vowels come together?
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?
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:
RUSSIA
Find the number of words formed by permuting all the letters of the following words:
EXERCISES
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 number of four digits can be formed with the digits 1, 3, 3, 0?
How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?
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?
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?
If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.
In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?
In how many ways can the letters of the word "INTERMEDIATE" be arranged so that:
the relative order of vowels and consonants do not alter?
Evaluate
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 all letters are used at a time
Find the number of permutations of n different things taken r at a time such that two specified things occur together?
Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.
Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.
