Maths-
General
Easy

Question

If blank to the power of 10 P subscript r equals 5040 then r is :

  1. 4
  2. 9
  3. 8
  4. 5

Hint:

To find the value of r fromblank to the power of 10 P subscript r equals 5040 we will first use the formula P with r below and n on top equals fraction numerator n factorial over denominator open parentheses n minus r close parentheses factorial end fraction then after equating we will find r.

The correct answer is: 4


    Given, blank to the power of 10 P subscript r equals 5040
    rightwards double arrow fraction numerator 10 factorial over denominator left parenthesis 10 minus r right parenthesis factorial end fraction equals 5040
rightwards double arrow fraction numerator 10 cross times 9 cross times 8 cross times 7 cross times 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator left parenthesis 10 minus r right parenthesis factorial end fraction equals 5040
rightwards double arrow fraction numerator 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator open parentheses 10 minus r close parentheses factorial end fraction equals 1
rightwards double arrow 6 factorial equals open parentheses 10 minus r close parentheses factorial
rightwards double arrow open parentheses 10 minus 4 close parentheses factorial equals open parentheses 10 minus r close parentheses factorial
rightwards double arrow r equals 4

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