A) \[31\]
B) \[32\]
C) \[63\]
D) \[64\]
Correct Answer: C
Solution :
Given, six identical balls. Total number of ways choose one or more identical balls \[{{=}^{6}}{{C}_{1}}{{+}^{6}}{{C}_{2}}{{+}^{6}}{{C}_{3}}{{+}^{6}}{{C}_{4}}{{+}^{6}}{{C}_{5}}{{+}^{6}}{{C}_{6}}\] \[{{=}^{6}}{{C}_{1}}{{+}^{6}}{{C}_{2}}{{+}^{6}}{{C}_{3}}{{+}^{6}}{{C}_{2}}{{+}^{6}}{{C}_{1}}+1\] \[=6+\frac{6\times 5}{2\times 1}+\frac{6\times 5\times 4}{3\times 2\times 1}+\frac{6\times 5}{2\times 1}+6+1\] \[=6+15+20+15+6+1=63\]
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