Maths-
General
Easy

Question

If blank to the power of n minus 1 end exponent C subscript 3 plus to the power of n minus 1 end exponent C subscript 4 greater than to the power of n C subscript 3 then

  1. n greater than 5
  2. n greater than 6
  3. n greater than 7
  4. n greater than 8

hintHint:

To solve for the value of n first we use blank to the power of n C subscript r space end subscript plus to the power of n C subscript r plus 1 end subscript equals to the power of n plus 1 end exponent C subscript r plus 1 end subscript then we will apply the formula of combination and then after simplifying using inequality we will get the answer.

The correct answer is: n greater than 7


    using blank to the power of n C subscript r space end subscript plus to the power of n C subscript r plus 1 end subscript equals to the power of n plus 1 end exponent C subscript r plus 1 end subscript
    If blank to the power of n minus 1 end exponent C subscript 3 plus to the power of n minus 1 end exponent C subscript 4 greater than to the power of n C subscript 3
    rightwards double arrow to the power of n minus 1 plus 1 end exponent C subscript 4 greater than to the power of n C subscript 3
rightwards double arrow to the power of n C subscript 4 greater than to the power of n C subscript 3
rightwards double arrow fraction numerator n factorial over denominator left parenthesis n minus 4 right parenthesis factorial 4 factorial end fraction greater than fraction numerator n factorial over denominator left parenthesis n minus 3 right parenthesis factorial 3 factorial end fraction
rightwards double arrow fraction numerator left parenthesis n minus 3 right parenthesis factorial 3 factorial over denominator left parenthesis n minus 4 right parenthesis factorial 4 factorial end fraction greater than 1
rightwards double arrow fraction numerator left parenthesis n minus 3 right parenthesis left parenthesis n minus 4 right parenthesis factorial 3 factorial over denominator left parenthesis n minus 4 right parenthesis factorial 4.3 factorial end fraction greater than 1
rightwards double arrow fraction numerator n minus 3 over denominator 4 end fraction greater than 1
rightwards double arrow n minus 3 greater than 4
rightwards double arrow n greater than 7

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