i need quick help with math!!!!!!!?

Question

lorenzo's pizzeria offer 10 different pizza topping, including pepperoni, garlic, pinapple, and black olive.
1. how many different three-topping pizza are possible?
2. how many different four-topping pizza are possible?
3.how many of the possible four-topping pizza do not include pepperoni or black olives?

please help!!!!!!
I am waiting you help.
thank you.

Answer 1

For three-item permutations, there are 10 possibilities for the first item, 9 for the second, 8 for the third. We can find the total number of different three-item permutations by multiplying 10 x 9 x 8 = 5040.

10_P_3 =

10! / (10 - 3)! =

10! / 7! =

(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (7 x 6 x 5 x 4 x 3 x 2 x 1)=

10 x 9 x 8 =

702 possible combinations of 3 toppings

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For four-item permutations, there are 10 possibilities for the first item, 9 for the second, 8 for the third, and 7 for the last item. We can find the total number of different four-item permutations by multiplying 10 x 9 x 8 x 7 = 720.

10_P_4 =

10! / (10 - 4)! =

10! / 6! =

(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (6 x 5 x 4 x 3 x 2 x 1)=

10 x 9 x 8 x 7 =

5040 possible combinations of four toppings.

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For four-item permutations, there are 8 possibilities for the first item, 7 for the second, 6 for the third and 5 for the fourth. We can find the total number of different four-item permutations by multiplying 8 x 7 x 6 x 5 = 1680.

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So all of your answers are as follows...

1) 3 combinations of 10 = 720
2) 4 combinations of 10 = 5040
3) 4 combinations of 8 = 1680

Answer 2

How many 1 topping pizzas are there? 10. How many 2 different topping pizzas? (10 * 9) / 2 (Because you have chosen the first one, but the order of choosing does not matter)

Similarly for (a) there's 10C3 = (10*9*8) / (1*2*3)
b)10C4 = (10*9*8*7) / (1*2*3*4)
c) 10C4 - 8C4

Search under the word combinatorics, to find out more.

Answer 3

1. 10*9*8=720 different
2. 10*9*8*7=5040
3. 8*7*6*5=1680

Answer 4

1`. 10*9*8/3*2*1
=120
2. 10*9*8*7/4*3*2*1
=210
3. 2*9*8*7*6/4*3*2*1

Answer 5

1) 12
2)16
3)8

Answer 6

look in your algebra book here's one how many words can you make out of alegebra i know how many but do you?

Answer 7

do ya own homework. its not our jod 2 answer ya got damn home work!!!!! excuse me 4 cursing.....

Answer 8

say ok will u try to make me feel better

Answer 9

Do ur own home work!