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Easy

Question

If scriptbase P subscript r end scriptbase presuperscript 8 equals to the power of 8 P subscript left parenthesis r plus 1 right parenthesis then r is :

  1. 8
  2. 6
  3. 5
  4. 7

Hint:

In the question we will use the formulablank to the power of n P subscript r equals fraction numerator n factorial over denominator open parentheses n minus r close parentheses factorial end fraction on both sides then we will simplify to get the value of r.

The correct answer is: 7


    G i v e n space to the power of 8 P subscript r equals blank to the power of 8 P subscript open parentheses r plus 1 close parentheses end subscript
rightwards double arrow fraction numerator 8 factorial over denominator open parentheses 8 minus r close parentheses factorial end fraction equals fraction numerator 8 factorial over denominator open parentheses 8 minus r minus 1 close parentheses factorial end fraction
rightwards double arrow fraction numerator 1 over denominator open parentheses 8 minus r close parentheses factorial end fraction equals fraction numerator 1 over denominator open parentheses 7 minus r close parentheses factorial end fraction
rightwards double arrow open parentheses 7 minus r close parentheses factorial equals open parentheses 8 minus r close parentheses factorial
rightwards double arrow open parentheses 7 minus 7 close parentheses factorial equals open parentheses 8 minus 7 close parentheses factorial space space space space space open square brackets 0 factorial equals 1 space a n d space 1 factorial equals 1 close square brackets
rightwards double arrow r equals 7

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