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Maths-

General

Easy

Question

If $blank to the power of 12 P subscript r equals to the power of 11 P subscript 6 plus 6 times to the power of 11 P subscript 5$ then r is :

6
5
7
8

hint Hint:

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

The correct answer is: 6

Given, $blank to the power of 12 P subscript r equals to the power of 11 P subscript 6 plus 6 times to the power of 11 P subscript 5$
$rightwards double arrow fraction numerator 12 factorial over denominator open parentheses 12 minus r close parentheses factorial end fraction equals fraction numerator 11 factorial over denominator open parentheses 11 minus 6 close parentheses factorial end fraction plus 6. fraction numerator 11 factorial over denominator open parentheses 11 minus 5 close parentheses factorial end fraction rightwards double arrow fraction numerator 12 factorial over denominator open parentheses 12 minus r close parentheses factorial end fraction equals 11 factorial open square brackets fraction numerator 1 over denominator 5 factorial end fraction plus 6 fraction numerator 1 over denominator 6 factorial end fraction close square brackets rightwards double arrow fraction numerator 12 cross times 11 factorial over denominator open parentheses 12 minus r close parentheses factorial end fraction equals 11 factorial open square brackets fraction numerator 1 over denominator 5 factorial end fraction plus fraction numerator 6 over denominator 5 factorial cross times 6 end fraction close square brackets rightwards double arrow fraction numerator 12 over denominator open parentheses 12 minus r close parentheses factorial end fraction equals fraction numerator 2 over denominator 5 factorial end fraction rightwards double arrow fraction numerator 6 over denominator open parentheses 12 minus r close parentheses factorial end fraction equals fraction numerator 1 over denominator 5 factorial end fraction rightwards double arrow 6 cross times 5 factorial equals open parentheses 12 minus r close parentheses factorial rightwards double arrow 6 factorial equals open parentheses 12 minus r close parentheses factorial rightwards double arrow r equals 6$

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