There are 4 daily flights from Palooka to Wichita and 6 daily flights from Wichita to Kalamazoo. How many different ways are there to fly from Palooka to Wichita one day, and then to Kalamazoo the following day?
Please show more than one approach.
Would I multiply 4 times 6?
Yes.
To find the number of different ways to fly from Palooka to Wichita and then to Kalamazoo, we can use the concept of combinations.
Approach 1: Using the multiplication principle
Step 1: Calculate the number of ways to fly from Palooka to Wichita.
Since there are 4 daily flights from Palooka to Wichita, there are 4 options to choose from.
Step 2: Calculate the number of ways to fly from Wichita to Kalamazoo.
Since there are 6 daily flights from Wichita to Kalamazoo, there are 6 options to choose from.
Step 3: Multiply the number of options from Step 1 with the number of options from Step 2.
4 options * 6 options = 24 different ways to fly from Palooka to Wichita and then to Kalamazoo.
Approach 2: Using the concept of combinations
Step 1: Determine the number of ways to choose a flight from Palooka to Wichita.
Since there are 4 daily flights and we need to choose 1, we can use the combination formula: nCr = n! / (r!(n-r)!).
In this case, n = 4 (number of flights from Palooka to Wichita) and r = 1 (number of flights we need to choose).
So, the number of ways to choose a flight from Palooka to Wichita is 4C1 = 4! / (1!(4-1)!) = 4! / (1! * 3!) = 4.
Step 2: Determine the number of ways to choose a flight from Wichita to Kalamazoo.
Since there are 6 daily flights and we need to choose 1, the number of ways to choose a flight from Wichita to Kalamazoo is 6C1 = 6.
Step 3: Multiply the number of ways from Step 1 with the number of ways from Step 2.
4 ways * 6 ways = 24 different ways to fly from Palooka to Wichita and then to Kalamazoo.
So, by using either the multiplication principle or the concept of combinations, we find that there are 24 different ways to fly from Palooka to Wichita one day and then to Kalamazoo the following day.