Assume that the camper has 4 jackets, 2 sleeping bags, and 11 different packages of food. An outfit consists of 2 jackets, 2 sleeping bags, and 7 packets of food.
How many ways can the trip be outfitted?
C(4,2) * C(2,2) * C(11,7) = 1980
To calculate the number of ways the trip can be outfitted, we need to find the combination of jackets, sleeping bags, and packets of food that can be chosen for the trip.
Since an outfit consists of 2 jackets, 2 sleeping bags, and 7 packets of food, we need to choose 2 jackets from 4, 2 sleeping bags from 2, and 7 packets of food from 11.
To find the number of ways to choose the jackets, we will use the combination formula:
C(n, r) = n! / (r!(n - r)!)
where C is the combination, n is the total number of items to choose from, and r is the number of items to be chosen.
Using this formula, the number of ways to choose 2 jackets from 4 is:
C(4, 2) = 4! / (2!(4-2)!)
= 4! / (2!2!)
= (4 * 3 * 2!) / (2! * 2!)
= (4 * 3) / 2
= 6
Similarly, the number of ways to choose 2 sleeping bags from 2 is:
C(2, 2) = 2! / (2!(2-2)!)
= 2! / (2! * 0!)
= 2! / 2!
= 1
Finally, the number of ways to choose 7 packets of food from 11 is:
C(11, 7) = 11! / (7!(11-7)!)
= 11! / (7!4!)
= (11 * 10 * 9 * 8!) / (7!4!)
= (11 * 10 * 9) / 6
= 165
To find the total number of ways to outfit the trip, we multiply the outcomes of each category together:
Total ways = Number of ways to choose jackets * Number of ways to choose sleeping bags * Number of ways to choose packets of food
= 6 * 1 * 165
= 990
Therefore, there are 990 different ways the trip can be outfitted.