Permutations And Combinations Question 154
Question: 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, then n equals [AMU 2002]
Options:
A) 4
B) 8
C) 16
D) 32
Correct Answer: AShow Answer
Answer:
Solution:
Þ $ ^{2n+1}C_0+2( ^{2n+1}C_1+{{}^{2n+1}}C_2+…{{+}^{2n+1}}C _{n} ) $ $ +{{}^{2n+1}}{C _{2n+1}}={2^{2n+1}} $
Þ $ 1+2(T)+1={2^{2n+1}}\Rightarrow 1+T=\frac{{2^{2n+1}}}{2}=2^{2n} $
Þ $ 1+255=2^{2n}\Rightarrow 2^{2n}=2^{8}\Rightarrow n=4 $ .
BETA
