English

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,

Advertisements
Advertisements

Question

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?

Advertisements

Solution

Each answer is an arrangement of the 6 items of column B keeping the order of column A fixed.
∴ Total number of answers = Number of arrangements of items in column B = 6P6 = 6! = 720

shaalaa.com
Factorial N (N!) Permutations and Combinations
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.3 [Page 29]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.3 | Q 24 | Page 29

RELATED QUESTIONS

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)


Prove that: n! (n + 2) = n! + (n + 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 P (n − 1, 3) : P (n, 4) = 1 : 9, find n.


If P (n, 5) : P (n, 3) = 2 : 1, find n.


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.


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?


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 words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?


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?


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.


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 out of the letters of the word, 'ORIENTAL', so that the vowels always occupy the odd places?


How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the vowels are always together?


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

all consonants come together?


m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]


How many three letter words can be made using the letters of the word 'ORIENTAL'?


Find the number of words formed by permuting all the letters of the following words:
INTERMEDIATE


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


In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?


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?


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


If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.


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:

\[\frac{^{n}{}{C}_r}{^{n - 1}{}{C}_{r - 1}} = \frac{n}{r}\]

Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

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


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 (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 


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 but first letter is a vowel?


Find the number of permutations of n distinct things taken together, in which 3 particular things must occur together.


Write the number of diagonals of an n-sided polygon.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×