Module 3: Lesson 3

 

Self-Check 4

 

Questions 15.a. and 16.b. on page 94

15.  
    1. 
       
       n = −4 or n = 5
       
       

       To solve this equation, substitute in the formula nPr. When the solutions are checked, n = −4 is not a solution because n must be a natural number. Therefore, the only solution is n = 5.

16.  
    2. 
       
       Divide both sides by 2 to simplify the expression.
       
       Expand 7! looking for the values that will multiply to 210. The values that will multiply to 210 are 7 × 6 × 5, so the expression becomes
       
       
        
       
       
       Then divide both sides by 210, which gives the equation
       
       The 4! in the numerator and the expression (7 − r)! must divide to 1, so r must equal 3.
       

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