Question

1. there is a set of 12 cards numbered 1 to 12. a card is chosen at random. event a is choosing a number than 6. event b is choosing a number divisible by 3. a diagram is given below.

determine the probability of the following. leave your answer in simplified fraction form. (1 point total)
a. ( p(a) )
b. ( p(b) )
c. ( p(acup b) )
d. ( p(acap b) )

1. there are 6 different colored pens in a box. each pen has a unique color. in how many orders can 4 pens be chosen? in other words, what is the number of permutations of picking 4 pens from the box? (lesson 19.2) (1 point)

a. 720
b. 360
c. 30

Explanation:

Step1: Use permutation formula

The formula for permutations \(P(n,r)=\frac{n!}{(n - r)!}\), where \(n = 6\) (total number of pens) and \(r=4\) (number of pens to be chosen).

Step2: Calculate factorial values

\(n!=6! = 6\times5\times4\times3\times2\times1=720\), \((n - r)!=(6 - 4)!=2!=2\times1 = 2\)

Step3: Substitute into formula

\(P(6,4)=\frac{6!}{(6 - 4)!}=\frac{720}{2}=360\)

Answer:

B. 360