# Math

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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.

1. A student must answer 7 of 10 questions on an exam. How many different sets of
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
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

• Math -

I am sorry I didn't realize it cut off

b) 4C2 x 48C3 = 103 776
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

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