Alock has 5 buttons. the lock is opened by pushing two buttons simultaneously and then by pushing one button alone. how many combinations are possible?

We first must calculate how many ways 2 oblects can be chosen from 5.

combinations = 5! / 2! * (5-2)!

combinations = 5*4 / 2

combinations = 10

There are 10 ways to choose the 2 buttons and 5 ways to choose the final butto so there are 10 * 5 = 50 different ways.

Source

1728.com/combinat.htm

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.