A) \[{{2}^{n-1}}\]
B) \[{{2}^{n}}-1\]
C) \[{{2}^{n-1}}-1\]
D) \[{{2}^{n}}\]
Correct Answer: A
Solution :
The required number of ways = The even number of\[0s\]i.e., \[\{0,\,\,2,\,\,4,\,\,6,...\}\] \[=\frac{n!}{n!}+\frac{n!}{2!(n-2)!}+\frac{n!}{4!(n-4)!}\] \[{{=}^{n}}{{C}_{0}}{{+}^{n}}{{C}_{2}}{{+}^{n}}{{C}_{4}}+...\,\,\,={{2}^{n-1}}\]
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