Advertisements
Advertisements
Question
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?
Advertisements
Solution
There are 4 different types of works.
∴ Number of arrangements of these 4 works, taken 4 at a time = 4!
Of these 4 works, two of the works with 3 volumes each can be arranged in 3! ways each and two of the works with 2 volumes each can be arranged in 2! ways.
Total number of arrangements = 4! x (3! x 3!) x (2! x 2!) = 3456
APPEARS IN
RELATED QUESTIONS
Convert the following products into factorials:
1 · 3 · 5 · 7 · 9 ... (2n − 1)
If (n + 1)! = 90 [(n − 1)!], find n.
If (n + 3)! = 56 [(n + 1)!], find n.
Prove that:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
If P (5, r) = P (6, r − 1), find r ?
If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.
In how many ways can five children stand in a queue?
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?
How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels come together?
How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?
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 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?
How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?
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.
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
How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?
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?
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?
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.
Find the total number of ways in which six ‘+’ and four ‘−’ signs can be arranged in a line such that no two ‘−’ signs occur together.
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)!
For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1
Prove that: 4nC2n : 2nCn = [1 · 3 · 5 ... (4n − 1)] : [1 · 3 · 5 ... (2n − 1)]2.
Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
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?
