An ice cream shop has a choice of 7 sundae toppings. suppose you could afford at least for toppings how many different ice cream's Sundays could you order
Assuming order of the toppings are not relevant, then you can order
7C4=7!/((7-4)!(4!)) Sundaes
=35
To find the number of different ice cream sundaes you can order, considering you can choose up to 4 toppings out of 7 options, you can use the concept of combinations.
A combination is a selection of items where the order does not matter. The formula to find the number of combinations, denoted as "nCk" or "C(n, k)", is:
nCk = n! / (k!(n-k)!)
Where "n!" represents the factorial of "n", which means multiplying all positive integers from 1 to "n".
In this case, the number of toppings to choose from is "n = 7", and you want to choose "k = 4" toppings. So let's calculate the number of combinations:
7C4 = 7! / (4!(7-4)!)
= 7! / (4!3!)
Calculating the factorials:
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
4! = 4 x 3 x 2 x 1 = 24
3! = 3 x 2 x 1 = 6
Substituting the factorials into the combination formula:
7C4 = 5040 / (24x6)
= 5040 / 144
= 35
So, you can order 35 different ice cream sundaes if you choose 4 toppings from a selection of 7.