Question

1. a newspaper editor is deciding which of 7 articles to print on the front page. 3a if she can only choose 3 of them for the front page, how many different selections are possible? = 35 5 well done! 3b if robert wrote one of the 7 articles, what is the probability his article is chosen for the front page? = enter your next step here

Explanation:

3b Solution:

Step1: Find favorable outcomes

To find the number of favorable outcomes (selections where Robert's article is chosen), we need to choose 2 more articles from the remaining 6 (since Robert's article is already included). Using the combination formula \( _nC_r=\frac{n!}{r!(n - r)!} \), where \( n = 6 \) and \( r=2 \):
\[
_6C_2=\frac{6!}{2!(6 - 2)!}=\frac{6!}{2!4!}=\frac{6\times5}{2\times1}=15
\]

Step2: Find total possible selections

From part 3a, we know the total number of ways to choose 3 articles from 7 is 35.

Step3: Calculate probability

Probability is the number of favorable outcomes divided by the total number of possible outcomes. So the probability \( P \) that Robert's article is chosen is:
\[
P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{15}{35}=\frac{3}{7}
\]

Answer:

\(\frac{3}{7}\)