Question

there are six bands competing in a competition. how many different ways can the 1st, 2nd, and 3rd place be awarded?
select one:
a. 6
b. 20
c. 30
d. 120

a quadrilateral with only one pair of parallel sides is called a
select one:
a. parallelogram
b. rectangle
c. trapezoid
d. rhombus

Explanation:

First Question

Step1: Identify permutation formula

We use permutations since order (1st,2nd,3rd) matters. The formula for permutations is $P(n,k)=\frac{n!}{(n-k)!}$, where $n=6$ (total bands), $k=3$ (places to award).

Step2: Substitute values into formula

$$P(6,3)=\frac{6!}{(6-3)!}=\frac{6!}{3!}$$

Step3: Calculate factorials and simplify

$$\frac{6\times5\times4\times3!}{3!}=6\times5\times4=120$$

A parallelogram, rectangle, and rhombus all have two pairs of parallel sides. A trapezoid is defined as a quadrilateral with exactly one pair of parallel sides.

Answer:

d. 120

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Second Question