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}=20\times 19\times 3 $ $ ^{20}C_5{{=}^{20}}C _{15}=19\times 17\times 16\times 3 $ $ ^{20}C_7{{=}^{20}}C _{13}=19\times 17\times 16\times 15 $ $ ^{20}C_9{{=}^{20}}C _{11}=19\times 17\times 13\times 11\times 5\times 8 $ 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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