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1. I have an amount of Rs. 10 lakh, which I went to invest in stocks of some companies. I always invest only amounts that are multiples of Rs 1 lakh in the stock of any company. If I can choose from among the stocks of five different companies, In how many ways can I invest the entire amount that I have?
This case can be represented as arranging ten balls and (5 - 1) four walls in the single row, which can be done in 14C4 ways. (The balls placed between every successive pair of walls belong to one group) 14C4 = 1001 ways.
Solution:
The situation is similar to placing 10 identical balls among 5 distinguishable boxes, where a box may have zero or more balls in it.This case can be represented as arranging ten balls and (5 - 1) four walls in the single row, which can be done in 14C4 ways. (The balls placed between every successive pair of walls belong to one group) 14C4 = 1001 ways.