1. Use elimination to eliminate y. You'll then get an equation in x only.

2. I thought of this in terms of combinations. There is only one possible favourite colour.

There are 63 ways of choosing colours, that is:

1 way of choosing all 6,

6C5 ways of picking 5 of 6 colours,

6C4 ways of picking 4 of 6 colours,

6C3 ways of picking 3 of 6 colours,

6C2 ways of picking 2 of 6 colours,

6C1 ways of picking 1 of 6 colours,

for a total of 63 ways.

3. Use the compound formula with subtraction:

4. The equation of the line is in the form:

Now, make a sketch of the curve

This will give you an indication on about how the problem is, that is, the line is actually a tangent to the circle with equation

Equate the two lines to get another quadratic equation.

Use the fact that if they have equal roots, then for . Substitute the values and solve for a.

5. Counting all will be the easiest method...

6. Find the exact opposite and subtract from the total number of ways ion which the letters can be arranged.

Post what you get!