Exercise 7 Page 703

We want to find the probability that your photo and your friend's photo are the two ones placed at the top of the page. To do so we will use theoretical probability. P=Favorable Outcomes/Possible Outcomes We will start by finding the number of possible outcomes, which is the number of combinations of 20 photos taken 2 at a time. This is because there are two places at the top of the page. Notice the order in which the photos at the top of the page are placed is not important. We are only interested in whose photos are chosen. _nC_r = n!/(n-r)! * r! We recalled the formula for the number of combinations of n objects taken r at a time. In our case, the total number of photos from which we can choose is 20, so n= 20. Out of them, we choose 2 photos to place at the top of the page. Therefore, we know that r = 2. Let's substitute these values and find the number of possible combinations.

_nC_r = n!/(n-r)! * r!

SubstituteII

n= 20, r= 2

_(20) C_2 = 20!/( 20- 2)! * 2!

▼

Evaluate right-hand side

SubTerm

Subtract term

_(20)C_2 = 20!/18! * 2!

Write as a product

_(20)C_2 = 20 * 19 * 18!/18! * 2!

CancelCommonFac

Cancel out common factors

_(20)C_2 = 20 * 19 * 18!/18! * 2!

SimpQuot

Simplify quotient

_(20)C_2 = 20 * 19/2!

2!=2

_(20)C_2 = 20 * 19/2

Multiply

Multiply

_(20)C_2 = 380/2

CalcQuot

Calculate quotient

_(20)C_2 = 190

Therefore, the number of possible outcomes is 190. Next, we will look for the number of favorable outcomes. Notice there is only one outcome that includes your photo and your friend's photo being chosen, so the number of favorable outcomes is 1. This means that we have enough information to calculate the desired probability. P=Favorable Outcomes/Possible Outcomes [0.9em] ⇕ P=1/190 The probability that your photo and your friend's photo are the two ones placed at the top of the page is 1190.