A) \[^{7}{{C}_{3}}.9{{+}^{7}}{{C}_{5}}.44{{+}^{7}}{{C}_{1}}.265\]
B) \[^{7}{{C}_{6}}.265{{+}^{7}}{{C}_{5}}.9{{+}^{7}}{{C}_{7}}.44\]
C) \[^{7}{{C}_{5}}.9{{+}^{7}}{{C}_{2}}.44{{+}^{7}}{{C}_{1}}.265\]
D) None of these
Correct Answer: A
Solution :
[a] No. of ways getting one correct \[{{=}^{7}}{{C}_{6}}6!\left( 1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+...+\frac{1}{6!} \right){{=}^{7}}{{C}_{1}}.265\] No. of ways getting two correct \[{{=}^{7}}{{C}_{2}}.5!\left( 1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+...-\frac{1}{5!} \right){{=}^{7}}{{C}_{2}}.44\] No. of ways getting three correct \[{{=}^{7}}{{C}_{3}}.4!\left( 1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!} \right){{=}^{7}}{{C}_{3}}.9\] Required no. of ways \[{{=}^{7}}{{C}_{3}}.9{{+}^{7}}{{C}_{2}}.44{{+}^{7}}{{C}_{1}}.265.\]
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