Maths-
General
Easy

Question

If 9P5 + 5 9P4 = 10Pr , then r =

  1. 4    
  2. 5    
  3. 9    
  4. 10    

Hint:

Use the formula P presuperscript n subscript r space equals space fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction

The correct answer is: 5


    Given : P presuperscript 9 subscript 5 space plus space 5 space cross times P presuperscript 9 subscript 4 space equals space P presuperscript 10 subscript r
    Using Formula :
    P presuperscript n subscript r space equals space fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction
    fraction numerator 9 factorial over denominator left parenthesis 9 minus 5 right parenthesis factorial end fraction space plus space 5 cross times fraction numerator 9 factorial over denominator left parenthesis 9 minus 4 right parenthesis factorial end fraction space equals space fraction numerator 10 factorial over denominator left parenthesis 10 minus r right parenthesis factorial end fraction
    fraction numerator 9 factorial over denominator 4 factorial end fraction space plus space 5 space cross times space fraction numerator 9 factorial over denominator 5 factorial end fraction space equals space fraction numerator 10 cross times 9 factorial over denominator left parenthesis 10 minus r right parenthesis factorial end fraction
    Dividing both sides by 9!
    fraction numerator 1 over denominator 4 factorial end fraction plus 5 cross times fraction numerator 1 over denominator 5 factorial end fraction space equals space fraction numerator 10 over denominator left parenthesis 10 minus r right parenthesis factorial end fraction
    fraction numerator 5 over denominator 5 factorial end fraction plus space fraction numerator 5 over denominator 5 factorial end fraction equals space fraction numerator 10 over denominator left parenthesis 10 minus r right parenthesis factorial end fraction
fraction numerator 10 over denominator 5 factorial end fraction space equals space fraction numerator 10 over denominator left parenthesis 10 minus r right parenthesis factorial end fraction
E q u a t i n g space t h e space d e n o m i n a t o r s
5 factorial space equals space left parenthesis 10 minus r right parenthesis factorial
5 space equals space 10 space minus space r
r space equals space 5

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