# Counting Principle

• Number of ways of selecting r objects out of n objects
• nCr
• n!/(r!)*(n-r)!
• Number of ways of giving r objects to n people, such that repetition is allowed
• Nr

# Question-Counting Principle

• In how many ways 3 stocks can be chosen out of 10 stocks in a portfolio? (Combination)
• Choosing 3 out of 10 stocks is basically the number of combinations of 3 objects out of 10
• Therefore, the number of ways are

• In how many ways 3 stocks can be sold, if the sold stock is bought back in the portfolio before the next stock is sold?
• First stock can be sold in 10 ways
• Second can be sold in again 10 ways
• Third stock can again be sold in 10 ways
• Therefore total number of ways become =103 = 1,000

Example

You wish to choose a portfolio of 3 bonds and 4 stocks from a list of 5 bonds and 8 stocks.
How many different 7 asset portfolio can you make from this list.
80
700
1,716
100,800

Solution

B.

Example

There are 10 sprinters in the Olympic finals. How many ways can the gold, silver, and bronze medals be awarded?
120
720
1,440
604,800

Solution

B.
10P3 = 720
Please note that this is a case of Permutation and not Combination.