REAL LIFE SITUATIONS
Ex #1: You toss a coin 3 times. HHH, HHT, HTH, THH, HTT, THT, TTH, TTT There is one combination that will give you 3 heads, three combinations with 2 heads and 1 tail, three combinations with 2 tails and 1 head, and one combination that will give you 3 tails.
1, 3, 3, 1
Does this look familiar?
It's the 3rd row of Pascal's Triangle!
Now we know that the numbers in each row of Pascal's triangle correspond with the number of combinations for getting heads and tails in a coin toss. The number of tosses correspond with the row number in Pascal's Triangle
It's the 3rd row of Pascal's Triangle!
Now we know that the numbers in each row of Pascal's triangle correspond with the number of combinations for getting heads and tails in a coin toss. The number of tosses correspond with the row number in Pascal's Triangle
Ex#2: What is the probability of getting exactly 3 heads with 5 coin tosses?
1. Since we are tossing the coin 5 times, look at row number 5 in Pascal's triangle as shown in the image to the right. This row shows the number of combinations 5 tosses can make.
2. The 1 represents the combination of getting exactly 5 heads. The 5 represents the number of ways you can get 4 heads and the 10 represents the number of ways you can get 3 heads. Vice versa for tails.
3. Adding all the numbers together, 1 + 5 + 10 + 10 + 5 + 1 = 32 <- this is the total number of combinations. There are 10 different combinations that will get you exactly 3 heads.
4. Therefore, 10/32 = 0.31 = 31%
There is a 31% chance of getting exactly 3 heads in 5 coin tosses!
2. The 1 represents the combination of getting exactly 5 heads. The 5 represents the number of ways you can get 4 heads and the 10 represents the number of ways you can get 3 heads. Vice versa for tails.
3. Adding all the numbers together, 1 + 5 + 10 + 10 + 5 + 1 = 32 <- this is the total number of combinations. There are 10 different combinations that will get you exactly 3 heads.
4. Therefore, 10/32 = 0.31 = 31%
There is a 31% chance of getting exactly 3 heads in 5 coin tosses!
Combination Problems
To find out how many combinations of an object are possible, you may choose to simply use the formula for nCr, or you can use Pascal's Triangle! Find row "n" in the triangle and column "r". This is your number of combinations. It's that easy!
Ex: You have 10 friends and you want to take 5 of them to the movies. How many different ways could you pick 5 friends?
Ex: You have 10 friends and you want to take 5 of them to the movies. How many different ways could you pick 5 friends?