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? = enter your next step here

Explanation:

Step1: Identify the combination formula

We use the combination formula \( _nC_r=\frac{n!}{r!(n - r)!} \), where \( n = 7 \) (total articles) and \( r=3 \) (articles to choose).

Step2: Substitute values into the formula

Substitute \( n = 7 \) and \( r = 3 \) into \( _nC_r \):
\( _7C_3=\frac{7!}{3!(7 - 3)!}=\frac{7!}{3!4!} \)

Step3: Expand the factorials

\( 7! = 7\times6\times5\times4! \), \( 3! = 3\times2\times1 \), so:
\( \frac{7\times6\times5\times4!}{3\times2\times1\times4!} \)

Step4: Simplify the expression

Cancel out \( 4! \) from numerator and denominator, then calculate \( \frac{7\times6\times5}{3\times2\times1}=\frac{210}{6} = 35 \)

Answer:

35