Question

You can order a pizza with up to 8 possible toppings. Which is greater? The number of possible pizzas you can get with only 3 toppings or the number of possible pizzas you can get with 5 toppings?

Answer 1

1st case = \(\large{^8C_3 \times 3!}\)
2nd case = \(\large{^8C_5\times 5!}\)

Since, \(\large{^nC_r = ^nC_{n-r}}\)

Thus:

\[\large{^8C_3 = ^8C_5}\]

Thus: 2nd case > 1st case

Answer 2

I have assumed these things:

1. All toppings are different.
2. When you say number of toppings on pizza, you mean the `exact` number of toppings.

Answer 3

3. Complete pizza = pizza base + topping(s) (with order of toppings important)

Answer 4

4. Different order of toppings mean different complete pizza

Answer 5

Why would the order of the toppings be important? :3

Answer 6

I know - "many assumptions" but that's what I can think of now.

Answer 7

Well I have not eaten many pizzas, so I am leaving that to you all

Answer 8

If order is not important then both have the same number

Answer 9

By the way, vishweshshrimali5
there's an easier way of writing
\[\Large ^nC_r\cdot r!\]
And that's
\[\Large ^nP_r\]
^.^

Answer 10

Yeah I realised that while typing that stuff but left it as it gave the same answers :)

But thanks.

Answer 11

I had not considered that the order in which the toppings are placed matters. So yes, you are right haha.

Answer 12

Would it matter, though?
Does the pizza look like some sort edible archery target? haha

Answer 13

It was just an amusing "trick" question I came across and thought it was fun but all the smart people came and knew I couldn't slide it past you guys haha.

Answer 14

It worked (I guess) :D !!

So, .... Kainui.... when are you going to offer me and Peter the pizzas we prepared

Answer 15

I'd love a slice :3

Answer 16

*number of pizzas we both found

Answer 17

brb lol

Answer 18

Hey thats not a pizza :P

Answer 19

who wants the ones with 5 toppings and who wants the ones with 3 toppings?

Answer 20

I want the one pizza with all 8 toppings.

Answer 21

Same here ^^^^^^^

Answer 22

How about I give you 1 pizza with 0 toppings, it's pretty much the same.

Answer 23

:/

Answer 24

lol