To win at LOTTO in one state, one must correctly select 6 numbers from a collection of 47 numbers (1 through 47). The order in which the selection is made does not matter. How many different selections are possible?

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.

Using only the digits 5, 6, 7, 8, how many different three digit numbers can be formed if no digit is repeated in a number?

What is the value of the discriminant, b2 ? 4ac, for the quadratic equation 0 = x2 ? 4x + 5, and what does it mean about the number of real solutions the equation has?