Could someone please help me out with the data homework? All I need is someone to check my answers. If any are incorrect could you please explain what I did wrong.

Question

1. A student must answer 7 of 10 questions on an exam. How many different sets of
questions can be answered if
a) there are no restrictions?
b) four of the first five questions must be answered?

a) 10C7 = 120 b) 5C4 x 5C3 = 50

2. A pizza can be ordered with any number of 8 different toppings OR with no toppings at
all.
a) Find the number of 4 topping orders available.
b) Find the total number of possible orders.

a) 8C4 = 70 b) 2^8 – 1 = 255

3. How many five-digit odd numbers can be formed from the digits of the number 5 390
462?

7C5 = 21
21 x 3/7
= 9

4. In the game of poker, each player is dealt a hand of five cards. How many hands contain
a) all hearts?
b) exactly 2 aces?
c) at least one diamond?
d) a full house?

a) 13C5 = 1287
b) 4C2 x 48C3 = 103 776
c) final answer = 2023203
d) 52C3 x 49C2 =

5. A club has 25 members. In how many ways can
a) a committee of 3 members be chosen?
b) the offices of president, vice-president, secretary, and treasurer be filled?
c) the members from (b) stand in line for a picture if the president and vicepresident
must stand side by side?

a) 25C3 = 2300
b) 25P3 = 13 800
c) 2(2!) = 4

6. In how many ways can 8 boys sit in a row if
a) there are no restrictions?
b) Jimmy and Bobby must be kept apart?

a) 8! = 40 320
b) 8! - 2(7!) = 30 240

Thank you so much

Answer 1

I am sorry I didn't realize it cut off

b) 4C2 x 48C3 = 103 776
c) final answer = 2023203
d) 52C3 x 49C2 = 5.

A club has 25 members. In how many ways can
a) a committee of 3 members be chosen?
b) the offices of president, vice-president, secretary, and treasurer be filled?
c) the members from (b) stand in line for a picture if the president and vicepresident
must stand side by side?

a) 25C3 = 2300
b) 25P3 = 13 800
c) 2(2!) = 4

6. In how many ways can 8 boys sit in a row if
a) there are no restrictions?
b) Jimmy and Bobby must be kept apart?

a) 8! = 40 320
b) 8! - 2(7!) = 30 240