SATHEE: Permutations And Combinations Question 360

Permutations And Combinations Question 360

Question: The greatest common divisor of $ ^{20}C_1{{,}^{20}}C_3,…{{,}^{20}}C _{19} $ is

Options:

A) 20

B) 4

C) 5

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

[b] $ ^{20}C_1{{=}^{20}}C _{19}=20 $ $ ^{20}C_3={{}^{20}}C _{17}= \frac{20\times 19\times 18}{3\times 2\times 1} $ $ ^{20}C_5{{=}^{20}}C _{15}= \frac{19\times 18\times 17\times 16\times 15}{5\times 4\times 3\times 2\times 1} $ $ ^{20}C_7{{=}^{20}}C _{13}= \frac{19\times 18\times 17\times 16\times 15\times 14\times 13}{7\times 6\times 5\times 4\times 3\times 2\times 1} $ $ ^{20}C_9{{=}^{20}}C _{11}= \frac{19\times 18\times 17\times 16\times 15\times 14\times 13\times 12\times 11}{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1} $ Clearly G.C.D. = 4

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Permutations And Combinations Question 360

Question: The greatest common divisor of $ ^{20}C_1{{,}^{20}}C_3,…{{,}^{20}}C _{19} $ is

Options:

Answer:

Solution:

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