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Let Pn denotes the number of ways in whi...

Let `P_n` denotes the number of ways in which three people can be selected out of 'n' people sitting in a row, if no two of them are consecutive. If `P_(n+1)- P_n=15` then the value of 'n` is____.

Text Solution

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`x_1+x_2+x_3+x_4=n-3`
We know`x_1=1+x_1',x_3=1+x_3'`
`x_1+x_2'+x_3'+x_4+2=n-3`
`x_1+x_2'+x_3'+x_4=n-5`
`P_n=.^(n-5+3)C_3=.^(n-2)C_3`
`P_(n+1)-P_n=15`
`.^(n-1)C_3-.^(n-2)C_3=15`
`((n-1)(n-2)(n-3))/(3*2)-((n-2)(n-3)(n-4))/(3*2)=15`
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