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If(56)P(r+6):(54)P(r+3)=30800 :1, find r...

If`(56)P_(r+6):`(54)`P_(r+3)`=30800 :1,` `find r`

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We have, `(.^(56)P_(r+6))/(.^(54)P_(r+3))=(30800)/(1)`
`implies(56)(55)(.^(54)P_(r+4))/(.^(54)P_(r+3))=(30800)/(1)` [from note (iii)]
`implies(.^(54)P_(r+4))/(.^(54)P_(r+3))=10`
`implies54-(r+4)+1=10` . . . . [from vote (v)]
`r=41`
`therefore.^(r)P_(2)=.^(41)P_(2)=41*40=1640`
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ARIHANT MATHS-PERMUTATIONS AND COMBINATIONS -Exercise (Questions Asked In Previous 13 Years Exam)
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