English

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?

Advertisements
Advertisements

Question

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?

Advertisements

Solution

Here, all the four books are to be arranged on a shelf. This means that we have to find the number of arrangements of the books, taken all at a time.
⇒ 4P4
Now, nPn = n!
Similarly, 4P4  = 4! = 24

shaalaa.com
Factorial N (N!) Permutations and Combinations
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.3 [Page 28]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.3 | Q 18 | Page 28

RELATED QUESTIONS

Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18


Convert the following products into factorials:

1 · 3 · 5 · 7 · 9 ... (2n − 1)


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 nP4 = 360, find the value of n.


If P (9, r) = 3024, find r.


If P (n, 4) = 12 . P (n, 2), find n.


If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.


From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?


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?


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?


All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.


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 permutations can be formed by the letters of the word, 'VOWELS', when
each word begins with E?


How many permutations can be formed by the letters of the word, 'VOWELS', when

all consonants come together?


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:
SERIES


How many words can be formed with the letters of the word 'UNIVERSITY', the vowels remaining together?


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 different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?


How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.


Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.


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?


Find the total number of permutations of the letters of the word 'INSTITUTE'.


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'.


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:

 nCr + 2 · nCr − 1 + nCr − 2 = n + 2Cr.


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 


Find the number of permutations of n different things taken r at a time such that two specified things occur together?


If 35Cn +7 = 35C4n − 2 , then write the values of n.


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 number of ways in which 5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×