Suppose you are making yourself a sandwich. how many different sandwiches can you make if you have four choices in bread, two choices in meat, and five choices in cheese?

Yum, sandwiches. The answer is 40, but I'll explain why.
For the sake of this question, I'll assume we're only going to be using one of each item. It doesn't matter what order they're in, since a sandwich with wheat, bacon, and chedder tastes the same as one with wheat, cheese and bacon. That makes this a combination.
Now it would be extremely easy just to say "multiply the numbers, and that's your answer", but that would be the easy way out. So I'll explain why this equation works.
First, you can choose from 4 types of bread. That gives us four options. After that, we can chose from 2 meats. That's 8 different combinations, and we haven't even added the cheese. So now we get to choose from 5 of those. If we took those 8 different sandwiches and made one of each with each kind of cheese, that gives us 40 sandwiches.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

I’m not absolutely sure but i think it’s 7x6x5x4x3x2=5040 because as the first character you can take any of the 7 given then you are left with 5 then 6 then 4 etc.