Question

When you open credit cards at a bank, you initiate a hard inquiry once you apply for credit. If you are approved for a credit card, this counts as a new account. Having too many hard inquiries and new accounts on your credit report lowers your credit score, so you’ll want to be judicious when you apply for additional lines of credit. Let’s say you’re interested in the following credit cards: •Chase Sapphire Reserve•Wells Fargo Propel Card•American Express Blue Cash Everyday •Citi Double Cash Card•Chase Freedom•Chase Amazon Prime Rewards Card•Bank of America Cash Rewards Visa•American Express Platinum Answer the following questions below (show work as applicable, using factorial notation if necessary):Scenario 2: Imagine you would like to apply for three of these credit cards. How many different ways could you apply for three credit cards out of this group, without taking order into account? _____________

Answer 1

Given the credit card options:

• Chase Sapphire Reserve

• Wells Fargo Propel Card

• American Express Blue Cash Everyday

• Citi Double Cash Card

• Chase Freedom

• Chase Amazon Prime Rewards Card

• Bank of America Cash Rewards Visa

• American Express Platinum

Then, there are 8 options.

If you want to apply for 3 credit cards and the order does not matter, you can use combination to see how many options you have.

The formula for combination of r elements out n elements is:

`C(n,r)=(n!)/((n-r)!*r!)`

In this question:

n = 8

r = 3

`\begin{gathered} C(n,r)=(8!)/((8-3)!*3!) \\ C(n,r)=(8!)/(5!*3!) \\ C(n,r)=(8*7*6*5!)/(5!*3*2) \\ C(n,r)=(8*7*6)/(3*2) \\ C(n,r)=56 \end{gathered}`

Answer: 56 ways.