A person going to a party was asked to bring 5 different bags of chips. Going to the store, she finds 14 varieties.
How many different selections can she make?
14C5 = ?
50
To calculate the number of different selections she can make, we need to use the combination formula for selecting items without considering the order.
The combination formula is given by:
C(n, r) = n! / (r!(n - r)!)
Where:
n = total number of items (14 varieties of chips in this case)
r = number of items to be selected (5 bags of chips in this case)
! = factorial (the product of all positive integers less than or equal to the number)
Plugging in the values:
C(14, 5) = 14! / (5!(14 - 5)!)
= 14! / (5! * 9!)
= (14 * 13 * 12 * 11 * 10) / (5 * 4 * 3 * 2 * 1)
= 2002
Therefore, she can make 2002 different selections of 5 bags of chips from the 14 varieties at the store.
To find the number of different selections she can make, we need to use the concept of combinations.
The formula for combinations is given by:
nCr = n! / ((n-r)! * r!)
Where n is the total number of items and r is the number of items to be selected.
In this case, the person has 14 varieties of chips to choose from, and she needs to select 5 bags. So, n = 14 and r = 5.
We can calculate this using the formula:
14C5 = 14! / ((14-5)! * 5!)
To simplify the calculation, we can cancel out some terms:
14! / ((14-5)! * 5!)
= 14! / (9! * 5!)
Now, we can calculate the factorial terms:
14! = 14 * 13 * 12 * 11 * 10 * 9!
We can now cancel out the 9! terms:
(14 * 13 * 12 * 11 * 10 * 9!) / (9! * 5!)
The 9! terms cancel out:
(14 * 13 * 12 * 11 * 10) / (5!)
Now, we can calculate the remaining factorial:
5! = 5 * 4 * 3 * 2 * 1
Calculating further, we get:
(14 * 13 * 12 * 11 * 10) / (5 * 4 * 3 * 2 * 1)
= (24024) / (120)
= 200
Therefore, the person can make 200 different selections of 5 bags of chips from 14 varieties.