MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
Satyaki Dutta Grade: 11
        

There are 2n people standing in a queue in front of a ticket booking office. n of those 2n people have a Rs 10 note each. Rest of the people have a Rs 5 note each. At first the man at the ticket booking office do not have any money. The price of each ticket being Rs 5, in how how many ways can the queue be arranged so that there is no problem in change?

6 years ago

Answers : (1)

mycroft holmes
270 Points
										

Label the people who have Rs. 5 with them as A and those with Rs.10 as B. You need a sequence of length 2n composed of n A's and n B's such that number of B's never exceeds the number of A's at any segment of the sequence taken from the initial point. That is called in combinatorics as a Dyck Sequence. 


 


The number of such sequences is the nth Catalan Number given by 


 


This is out of your syllabus, but of your interested you can consult the wiki article http://en.wikipedia.org/wiki/Catalan_number

6 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details

Ask Experts

Have any Question? Ask Experts

Post Question

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