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If .^(15)C(r): .^(15)C(R-1) = 11:5, then...

If `.^(15)C_(r): .^(15)C_(R-1) = 11:5`, then find the value of 'r'.

Text Solution

Verified by Experts

`.^(15)C_(r): .^(15)C_(r-1) = 11:5`
`rArr (.^(15)C_(r))/(.^(15)C_(r-1)) = (11)/(5)`
`rArr (15!)/(r!(15-r)!) ((r-1)!(16-r)!)/(15!) = (11)/(15)`
`rArr ((r-1)!(16-r)(15-r)!)/(r(r-1)!(15-r)!) =(11)/(5)`
`rArr (16-r)/(r) = (11)/(5)`
`rArr 11r = 80 - 5r`
`rArr r = 5`.
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