A) \[^{16}{{C}_{7}}\]
B) \[^{17}{{C}_{7}}\]
C) \[^{17}{{C}_{8}}\]
D) \[^{16}{{C}_{8}}\]
Correct Answer: B
Solution :
\[^{14}{{C}_{7}}+\sum\limits_{i=1}^{3}{^{17-i}{{C}_{6}}}{{=}^{14}}{{C}_{7}}{{+}^{14}}{{C}_{6}}{{+}^{15}}{{C}_{6}}{{+}^{16}}{{C}_{6}}\] \[{{=}^{15}}{{C}_{7}}{{+}^{15}}{{C}_{6}}{{+}^{16}}{{C}_{6}}{{=}^{16}}{{C}_{7}}{{+}^{16}}{{C}_{6}}{{=}^{17}}{{C}_{7}}\]
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