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

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

Text Solution

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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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