Permutations And Combinations Question 87
Question: If $ ^{2n}C_3:{{}^{n}}C_2=44:3 $ , then for which of the following values of $ r $ , the value of $ ^{n}C _{r} $ will be 15 [MP PET 1981]
Options:
A) $ r=3 $
B) $ r=4 $
C) $ r=6 $
D) $ r=5 $
Correct Answer: B $ \Rightarrow $ $ n $ $ \Rightarrow 4(2n-1)=44 $ $ \Rightarrow $ $ 2n=12 $ $ \Rightarrow $ $ n=6 $ Now $ ^{6}C _{r}=15 $ $ \Rightarrow $ $ ^{6}C _{r}{{=}^{6}}C_2 $ or $ ^{6}C_4 $ $ \Rightarrow $ $ r=2,\ 4 $ .
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Answer:
Solution:
BETA
