MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Yogita Nain Grade:
        

Hello frnds..........i m yogita....preparing for iit jee-2012


 


Can anybody give me the proof for dearrangement series in permutations..........??????

6 years ago

Answers : (1)

SAGAR SINGH - IIT DELHI
879 Points
										

Dear yogita,


Any change in the existing order of things is called a derangement.


If 'n' things are arranged in a row, the number of ways in which they can, be deranged so that none of them occupies its original place is


 derangements                         


 and it is denoted by D(n).


A question on derangement can be of the following kind:


Illustration:


Supposing 4 letters are placed in 4 different envelopes. In how many ways can be they be taken out from their original envelopes and distributed among the 4 different envelopes so that no letter remains in its original envelope?


Solution:


Using the formula for the number of derangements that are possible out of 4 letters in 4 envelopes, we get the number of ways as :


 4!(1 - 1 + 1/2! - 1/3! + 1/4!) = 24(1 - 1 + 1/2 - 1/6 + 1/24) = 9.


 

















We are all IITians and here to help you in your IIT JEE preparation.

All the best.


 If you like this answer please approve it....


win exciting gifts by answering the questions on Discussion Forum


 





Sagar Singh


B.Tech IIT Delhi
















6 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete AIPMT/AIIMS Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details
Get extra Rs. 6,837 off
USE CODE: JYOTI
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details
Get extra Rs. 6,837 off
USE CODE: JYOTI

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details