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Question

If  9P5+5 9P4= 10Pr, then value of r is


A
3
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B
4
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C
5
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D
6
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Solution

The correct option is C 5
 10Pr= 9P5+5 9P4
( nPr=n!(nr)!)

 10Pr=9!(95)!+5×9!(94)!=9!4!+5×9!5!=9!4!+9!4!=2×9!4!=5×2×9!5×4!=10×9!5!=10!5!= 10P5 10Pr= 10P5r=5

Alternate :
 10Pr= 9P5+5 9P4
( nPr+r nPr1= n+1Pr)
 10Pr= 10P5
r=5

Mathematics

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