How many different ways can you choose 3 frozen yogurt toppings from 20?
6,840
1,140
60*
2,260
I think it is 60 because 3*20 however not positive.
Number of choices
= C(20,3) = 1140
or , the long way....
If we consider order, the number of permutations is
20 x 19 x 18 = 6840
but the order should not matter , and each a 3 yogurt choice can be arranged in 3x2x1 or 6 ways, so we have to divide the above by 6
number of ways to choose = 6840/6 = 1140
Well, my friend, your calculation is close but quite frosty! The correct answer is 1,140.
To choose 3 frozen yogurt toppings from 20, we use a combination formula. The formula goes like this: 20 choose 3, which can be represented as C(20, 3). Using this formula, we get:
C(20, 3) = 20! / (3!(20-3)!) = 20! / (3!17!) = (20 × 19 × 18) / (3 × 2 × 1) = 1,140.
So, it looks like you dropped a scoop of yogurt there, but don't worry, it happens to the best of us. Keep your toppings high and your spirits higher!
To find the number of different ways you can choose 3 frozen yogurt toppings from 20, you can use the combination formula, which is given by:
C(n, r) = n! / (r!(n-r)!)
In this case, n = 20 (the number of available toppings) and r = 3 (the number of toppings to be chosen).
Plugging these values into the formula, we get:
C(20, 3) = 20! / (3!(20-3)!)
= 20! / (3!17!)
Calculating the factorials:
20! = 20 x 19 x 18 x 17!
3! = 3 x 2 x 1
Substituting these values into the formula:
C(20, 3) = (20 x 19 x 18 x 17!) / (3 x 2 x 1 x 17!)
The 17! terms cancel out, leaving us with:
C(20, 3) = (20 x 19 x 18) / (3 x 2 x 1)
= 1140
Therefore, the correct answer is 1,140.
To solve this problem, you need to use the combination formula. The formula for combinations is given by:
C(n, r) = n!/[(r!(n-r)!)]
In this case, you want to choose 3 frozen yogurt toppings from a set of 20 toppings. So, the values for n and r are:
n = 20 (total number of toppings)
r = 3 (number of toppings to choose)
Now, let's calculate the number of combinations:
C(20, 3) = 20! / [(3!(20-3)!)]
= 20! / (3! * 17!)
= (20 * 19 * 18 * 17!) / (3 * 2 * 1 * 17!)
As you can see, the (17!) terms in the numerator and denominator cancel out, leaving:
C(20, 3) = (20 * 19 * 18) / (3 * 2 * 1)
= 1140
So, there are 1,140 different ways to choose 3 frozen yogurt toppings from a set of 20 toppings. Therefore, option 2,260 is incorrect.