A carton contains 12 eggs of which 1 is bad. How many ways can you select 3 good eggs.?
1,2,3
2,3,4
3,4,5
4,5,6
To 11,1,2.
11 different ways.
do they have to be in sequence? Why not, say, 2,9,10 ?
11C3=11!/(11-3)!3! =165ways
To find the number of ways to select 3 good eggs from a carton that contains 12 eggs with 1 bad egg, we can use the concept of combinations.
The number of ways to select 3 good eggs can be calculated using the formula for combinations:
C(n, k) = n! / (k! * (n - k)!)
where n is the total number of eggs and k is the number of eggs to be selected.
In our case, we have a total of 12 eggs, out of which we need to select 3 good eggs.
C(12, 3) = 12! / (3! * (12 - 3)!)
Simplifying further:
C(12, 3) = 12! / (3! * 9!)
Now, let's calculate each factorial:
12! = 12 * 11 * 10 * 9!
3! = 3 * 2 * 1
Substituting the factorials in the combination formula:
C(12, 3) = (12 * 11 * 10 * 9!) / ((3 * 2 * 1) * 9!)
Canceling out the common terms:
C(12, 3) = 12 * 11 * 10 / (3 * 2 * 1)
C(12, 3) = 220
Therefore, there are 220 ways to select 3 good eggs from the carton.