how many different ways can you choose 3 vowels out of the box, if there are 5 vowels in the box and the order does NOT matter? a. 10 b. 15 c. 30 d. 60
D?
Your answer would be the case if the order DID matter
the correct answer is C(5,3) = 10
in detail it would be
5!/(3!,2!)
oh, thank you reiny!!!!
60
How many different ways can you choose 3 vowels out of the box, if there are 5 vowels in the box and order does not matter.
To find the number of different ways to choose 3 vowels out of a box with 5 vowels, where the order does not matter, you can use the combination formula. The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items to choose from, r is the number of items being chosen, and "!" denotes the factorial function.
In this case, n = 5 (total number of vowels) and r = 3 (number of vowels to be chosen). Plugging those values into the formula, we get:
C(5, 3) = 5! / (3!(5-3)!)
= 5! / (3!2!)
Calculating the factorials:
5! = 5 x 4 x 3 x 2 x 1 = 120
3! = 3 x 2 x 1 = 6
2! = 2 x 1 = 2
Plugging the factorial values back into the formula:
C(5, 3) = 120 / (6 x 2)
= 120 / 12
= 10
Therefore, there are 10 different ways to choose 3 vowels out of the box.
So, the correct answer is a. 10.