Advertisements
Advertisements
प्रश्न
There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?
Advertisements
उत्तर
Total number of books = 12
∴ Required number of arrangements = Arrangements of 12 things of which each of the 4 different books has three copies =\[\frac{12!}{3!3!3!3!}\]=\[\frac{12!}{(3! )^4}\]
APPEARS IN
संबंधित प्रश्न
If \[\frac{(2n)!}{3! (2n - 3)!}\] and \[\frac{n!}{2! (n - 2)!}\] are in the ratio 44 : 3, find n.
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.
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
If P (n, 5) : P (n, 3) = 2 : 1, 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 n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.
Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.
How many three-digit numbers are there, with distinct digits, with each digit odd?
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?
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 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 O and ends with L?
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:
INTERMEDIATE
In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?
How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?
In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?
Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.
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?
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?
Prove that the product of 2n consecutive negative integers is divisible by (2n)!
Evaluate
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, 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 value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]
Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.
