Assume that the camper has 3 jackets, 3 sleeping bags, and 11 different packages of food. An outfit consists of 1 jacket, 2 sleeping bags, and 4 packets of food.How many ways can the trip be outfitted?
thank you so much!
To determine the number of ways the trip can be outfitted, we can use the concept of combinations.
First, we need to choose 1 jacket from the 3 available. This can be done in 3 ways.
Next, we need to choose 2 sleeping bags from the 3 available. Since the order doesn't matter, we can use combinations to calculate this. The number of ways to choose 2 sleeping bags from 3 is 3C2 = 3.
Finally, we need to choose 4 packets of food from the 11 available. Again, using combinations, the number of ways to choose 4 packets of food from 11 is 11C4 = 330.
To find the total number of ways the trip can be outfitted, we multiply the number of choices for each category: 3 jackets * 3 sleeping bags * 330 packets of food = 2,970.
Therefore, there are 2,970 ways to outfit the trip.
To find the number of ways the trip can be outfitted, we can use the concept of combinations.
Let's break it down step by step:
Step 1: Choosing the jacket
Since there are 3 jackets available, we have 3 choices for the jacket.
Step 2: Choosing the sleeping bags
We need to choose 2 out of the 3 sleeping bags available. This can be calculated using combinations. The number of ways to choose 2 sleeping bags out of 3 is given by the formula 3C2, which is equal to 3.
Step 3: Choosing the packets of food
We need to choose 4 packets of food out of the 11 available. Similarly, the number of ways to choose 4 packets of food out of 11 is given by the formula 11C4.
Step 4: Combining the choices
To find the total number of ways the trip can be outfitted, we need to multiply the number of choices from each step. Therefore, the total number of ways is 3 (choices for jackets) * 3 (choices for sleeping bags) * 11C4 (choices for packets of food).
To calculate 11C4, we can use the combination formula: nCr = n! / (r!(n-r)!)
Plugging in the values, we get 11C4 = 11! / (4!(11-4)!) = 11! / (4!7!) = (11*10*9*8) / (4*3*2*1) = 330
So, the total number of ways the trip can be outfitted is 3 * 3 * 330 = 2970 ways.
jacket | sleeping bag, sleeping bag | food, food, food
number of ways
= 3 x (3x2) x (11x10x9x8)
= 142560