Problem Solving

Here I will post some interesting arrangements problems. The answers will be given later

1. There are six cars, two red, one yellow, one blue, one white, and one black. The cars are lined up in a row and cars of the same color have no difference. How many different arrangements are there so that two red cars are NOT next to each other?
(A) 720
(B) 600
(C) 480
(D) 240
(E) 120

2. Seven students, including Tom and Jerry, are to be selected a 3-people committee. If Tom and Jerry cannot be selected at the same time, in how many ways can the committee be selected?
(A) 20
(B) 28
(C) 30
(D) 35
(E) 40


3. How many free-digit numerals begin with the digit that represents a prime number and end with the digit that represents a prime number?
(A) 16
(B) 80
(C) 160
(D) 180
(E) 240


4. In how many ways can four boys and four girls be assigned seats in a row of eight seats if boys and girls are to alternate?
(A) 2!*4!*4!
(B) 4!*4!
(C) 2*4!
(D) 8!/2
(E) 8!

5. 123. How many 2-digit positive integers are there in which the sum of two digits is a 2-digit prime number?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20