1.

(i) If `""^(15)P_(r)=2730,` find the value of r. (ii) If ` ""^(10)P_(r)=5040,` find the value of r.

Answer» We have
(i) ` ""^(15)P_(r)=2730`
`rArr ""^(15)P_(r)=15xx 182`
`rArr ""^(15)P_(r)=15xx14xx13 " " ` ( up to 3 factors )
`rArr r =3.`
Hence, `r =3.`
(ii) ` ""^(10)P_(r)=5040`
`rArr ""^(10)P_(r)=10xx504`
`rArr ""^(10)P_(r)=10xx9xx56`
`rArr ""^(10)P_(r)=10xx9xx8xx7 " " `(up to 4 factors)
`rArr r =4.`
Hence, `r =4.`


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