1. How many eight digit even numbers are possible with the digits 7 5 4 5 7 5 0 7?

Question

Is the correct answer 240? If not, please explain.

2. Express t(6,3) + t(6,2) as a single term from Pascal's Triangle.

*The (6,3) and (6,2) are subscripts of t.

Answer 1

1. number is even, so last digit must be 0 or 4

That leaves 7 other digits, with 3 5's and 3 7's.

So, we have 7!/3!3! * 2 = 280
How did you get 240?

each term in the triangle is the sum of the two terms above. So, we have

t(7,3)

Answer 2

Why do you multiply 7!/3!3! by 2?

Answer 3

because the last digit can be chosen in 2 ways: 0 or 4.