Consider the set A = {2, {3, 4}, 3, 6, −1}. For each of the following propositions, indicate whether it is true or false

 1)Consider the set A = {2, {3, 4}, 3, 6, −1}. For each of the following propositions, indicate whether it is true or false.
(a) 3 ∈ A
(b) {3} ⊆ A
(c) {4, 3} ∈ A
(d) {3, 4} ⊆ A
(e) {3, −1} ⊆ A
(f ) 4 ∈ A
(g) {4} ⊆ A
(h) {3, −1, 2} ⊂ A 

2. A,B,C,D,E,F,G and H go to the rock concert. In how many ways can they be seated if:
a. they decide to sit boy-girl-boy-girl-boy-girl
b. the men must sit together and the women must sit together

3. The village of birbeck is conducting its weekly pick 4. They place 5 balls marked 1,2,3,4 and 5 in each of four plastic cylinders. The oldest person in town picks one ball form each cylinder. How many outcomes are possible?

4. When using a standard deck of playing cards, in how many ways can you get three of a kind?

5. Hank is giving away his collection of six radio controlled cars to his 4 little brothers. In how many ways can he distribute the cars if he has promised the police car to jimmy and the dump truck to Carl?

6. the computer store just received a shipment of 20 computers. Historically, we know that 4 of the 20 will break down before the warranty is up Creative web site purchases five of these computers. In how many ways can the shipment to creative web sites include:
a. exactly 3 computers that will break down before the warranty is up
b. exactly 3 computers that will break down before the warranty is up

7. Using the digit set (0,1,2,3,4) how many 4 digit numbers can be formed if:...(0xxx is not a number)
a. the number must end in 0

b. the number must have two zero's and no other repeated digit