In how many ways can an investor select five mutual funds for his investment portfolio from a recommended list of nine mutual funds?
What is C(9,5) ?
(choose 5 of nine)
Oh, the possibilities are endless! Well, not really, but close enough. Let's see, to calculate the number of ways an investor can select five mutual funds from a recommended list of nine, we can use the combination formula. So, it would be like choosing exotic fruits for a fruit salad, but instead, we're choosing mutual funds for an investment smoothie.
Using the formula, the number of ways to select five mutual funds from a list of nine would be calculated as: 9 choose 5, which can be written as 9C5.
And if we do a little math magic, we find that 9C5 equals 9!/5!(9-5)! which equals...wait for it...126!
So, brace yourself for the investing adventure, my friend, because you have 126 different combinations to choose from! Happy fund selection!
To calculate the number of ways an investor can select five mutual funds from a recommended list of nine mutual funds, we will use the combination formula.
The combination formula is given by:
C(n, r) = n! / (r! * (n - r)!)
Where:
n is the total number of options (9 in this case),
r is the number of choices (5 in this case),
! represents the factorial operation.
Plugging in the values, we get:
C(9, 5) = 9! / (5! * (9 - 5)!)
= 9! / (5! * 4!)
= (9 * 8 * 7 * 6 * 5!) / (5! * 4 * 3 * 2 * 1)
= (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)
= 9 * 2 * 7
= 126
Therefore, there are 126 different ways the investor can select five mutual funds from the recommended list of nine mutual funds.
To determine the number of ways an investor can select five mutual funds from a recommended list of nine, you can use the concept of combinations.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of items (in this case, the total number of mutual funds)
- r is the number of items to be chosen (in this case, the number of mutual funds to be selected)
Applying this to the given scenario, we have:
- n = 9 (the total number of mutual funds)
- r = 5 (the number of mutual funds to be selected)
Using the formula, we can calculate:
C(9, 5) = 9! / (5!(9-5)!)
= 9! / (5! * 4!)
= (9 * 8 * 7 * 6 * 5!) / (5! * 4 * 3 * 2 * 1)
= (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)
= 3024 / 24
= 126
Therefore, there are 126 different ways the investor can select five mutual funds from the recommended list of nine.