1.

(a) If `.^(22)P_(r+1):^(20)P_(r+2)=11 : 52`, find r. (b) If `.^(56)P_(r+6):^(54)P_(r+3)=30800: 1`, find r.

Answer» Correct Answer - 41
Given,
`.^(22)P_(r+1):^(20)P_(r+2)=11:52`
or `(22!)/((21-r)!):(20!)/((18-r))=11:52`
or `(22!)/((21-r)!)xx((18-r)!)/(20!)=(11)/(52)`
or `(22xx21xx20)/((21-r)(20-r)(19-r))=(11)/(52)`
or `(21-r)(20-r)(19-r)=2xx21xx52`
or `(21-r)(20-r)(19-r)=2xx3xx7xx4xx13`
or r=7
(b) `.^(56)P_(r+6): .^(34)P_(r+3)=30800:1`
or `(56!(51-r)!)/((50-r)!54!)=30800`
or `56xx55xx(51-r)=30800`
or r=41


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