Question

1. -/1 points

in how many ways can an investor select three mutual funds for his investment portfolio from a recommended list of ten mutual funds?
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1. -/1 points

in how many ways can six people boarding a bus be seated if the bus has seven vacant seats?
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Explanation:

Step1: Identify combination for Q5

We use combinations since the order of selecting mutual funds does not matter. The formula for combinations is $C(n,k)=\frac{n!}{k!(n-k)!}$, where $n=10$ (total funds) and $k=3$ (funds to select).
$C(10,3)=\frac{10!}{3!(10-3)!}=\frac{10!}{3!7!}$

Step2: Simplify combination for Q5

Cancel out $7!$ from numerator and denominator:
$\frac{10\times9\times8}{3\times2\times1}=120$

Step3: Identify permutation for Q6

We use permutations since the order of seating matters. The formula for permutations is $P(n,k)=\frac{n!}{(n-k)!}$, where $n=7$ (total seats) and $k=6$ (people to seat).
$P(7,6)=\frac{7!}{(7-6)!}=\frac{7!}{1!}$

Step4: Calculate permutation for Q6

$7!=7\times6\times5\times4\times3\times2\times1=5040$

Answer:

1. 120 ways
2. 5040 ways