how do i start to solve this
Harry has a choice of a veggie burge and a regular pizza
he can have three toppings his choices are
lettuce pickles onions tomatos and sprouts that is five items
how many combinations can he have
I think i multiply 5 x 3 and get 15 can you tell me is this right
First topping:
5 choices
sEcond choices 4 toppings
third choice 3 toppings
Answer: 5*4*3
nCr= N!/(n-r)!
To solve this problem, you need to use the concept of combinations, specifically the formula for finding combinations when order doesn't matter. The formula is as follows:
nCr = n! / (r!(n-r)!)
In this case, there are 5 toppings available (lettuce, pickles, onions, tomatoes, and sprouts) and Harry can choose 3 toppings. So, you want to calculate 5C3.
Now, let's break down the calculation step by step to find the number of combinations:
1. Calculate the factorial of the total number of choices (n):
n! = 5! = 5 x 4 x 3 x 2 x 1 = 120
2. Calculate the factorial of the chosen number of toppings (r):
r! = 3! = 3 x 2 x 1 = 6
3. Calculate the factorial of the remaining toppings (n-r):
(n-r)! = (5-3)! = 2!
4. Simplify the expression:
5C3 = 5! / (3!(5-3)!) = 5! / (3!2!) = 120 / (6 x 2) = 120 / 12 = 10
So, the correct answer is 10 combinations that Harry can have.
To summarize, you should use the combination formula nCr = n! / (r!(n-r)!) to solve this problem. Calculate the factorials of the individual components and simplify the expression to find the correct answer.