Ivan has a 5-cent stamp, a 10-cent stamp, and a 20-cent stamp.How many different combinations of postage can he form with the stamps?
3! is a nice number here.
Oh, you might not know about factorials yet.
3*2*1 is a nice number then.
There are 2^3-1 = 7 ways to choose at least one stamp.
To find out how many different combinations of postage Ivan can form with the stamps, we can consider all possible ways of using or not using each stamp.
One way to approach this problem is by using the concept of combinations. A combination is a selection of items without considering their order. In this case, we have three stamps, and we want to determine how many different combinations we can form using these stamps.
To find the number of combinations, we can use the formula for combinations, which is given by:
nCr = n! / (r!(n-r)!)
Where:
- n is the total number of stamps (in this case, 3).
- r is the number of stamps we choose to use.
In our case, we want to find the combinations using all possible values of r. So we need to find nCr for r = 0, 1, 2, and 3.
Let's calculate the different combinations:
For r = 0:
3C0 = 3! / (0!(3-0)!) = 3! / (0!3!) = 1
For r = 1:
3C1 = 3! / (1!(3-1)!) = 3! / (1!2!) = 3
For r = 2:
3C2 = 3! / (2!(3-2)!) = 3! / (2!1!) = 3
For r = 3:
3C3 = 3! / (3!(3-3)!) = 3! / (3!0!) = 1
Therefore, Ivan can form a total of (1 + 3 + 3 + 1) = 8 different combinations of postage using the 5-cent, 10-cent, and 20-cent stamps.