An advisor offers 8 mutual funds in the high risk category, 7 moderate, 10 in low risk.
The investor decides to invest in 3 high risk, 4 moderate risk, and 10 low risk. How many ways can he do this?
8*7*6*7*6*5*4*10!
or
8!/(8-3)! * 7!/(7-4)! * 10!/(10-10)!
To find the number of ways the investor can choose mutual funds from each risk category, we can use the concept of combinations.
In this case, we need to find the number of ways to choose 3 mutual funds from the high risk category, 4 mutual funds from the moderate risk category, and 10 mutual funds from the low risk category.
The number of ways to choose objects from a set without considering their order is given by the combination formula:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of objects and r is the number of objects to be chosen.
For the high risk category, there are 8 mutual funds and we need to choose 3. So the number of ways to choose 3 mutual funds from 8 is C(8, 3).
C(8, 3) = 8! / (3!(8-3)!) = 8! / (3!5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56
Similarly, for the moderate risk category, there are 7 mutual funds and we need to choose 4. So the number of ways to choose 4 mutual funds from 7 is C(7, 4).
C(7, 4) = 7! / (4!(7-4)!) = 7! / (4!3!) = (7 * 6 * 5) / (3 * 2 * 1) = 35
For the low risk category, there are 10 mutual funds and we need to choose 10. So the number of ways to choose 10 mutual funds from 10 is C(10, 10).
C(10, 10) = 10! / (10!(10-10)!) = 10! / (10!0!) = 1
To find the total number of ways to choose mutual funds from all three risk categories, we multiply the number of ways from each category:
Total number of ways = C(8, 3) * C(7, 4) * C(10, 10)
= 56 * 35 * 1
= 1,960
Therefore, there are 1,960 ways the investor can invest in 3 high-risk, 4 moderate-risk, and 10 low-risk mutual funds.