A receipt contains 3 ingredients, In how many different orders can all the ingredients be added.
3!=3 x 2=
To find the number of different orders in which the 3 ingredients can be added to a receipt, we can use the concept of permutations.
Permutations calculate the number of different arrangements or orders of a given number of items.
To find the number of permutations, we will use the formula for permutations of n items taken r at a time:
P(n, r) = n! / (n-r)!
In this case, we have 3 ingredients (n=3) and we want to find the different orders of all the ingredients, which means we want to take all 3 ingredients at a time (r=3).
Plugging these values into the formula:
P(3, 3) = 3! / (3-3)!
= 3! / 0!
The factorial of a number (n!) is the product of all positive integers from 1 to n.
3! = 3 x 2 x 1 = 6
0! = 1 (by definition)
Plugging these values into the equation:
P(3, 3) = 6 / 1
= 6
Therefore, there are 6 different orders in which all the ingredients can be added to the receipt.