Q)
(chatquestion)...llustration 6.96 A person is permitted to select at least one
and at most n coins from a collection of (2n + 1) distinct
coins. If the total number of ways in which he can select
coins is 255, find the value of n.
Sol. We have,
2n+C, + 2n+C, + ...
+ 2n*C, = 255
Also the sum of binomial coefficients is
(1)
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2nt Cntl
"Cy0el
2n+ C, + 2n+C, + … + 2n+lC, +
= (1 + 1)²*+1 = 22
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= 22n+1
2n+1 C 2n41
Co+2(²n+!C, + 2n\C, + …· + 2n+\ C,) +
1+ 2(zɔɔ) + 1 = 22n +
1+ 255 = 22
22n = 2 or n = 4
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