Permutations And Combinations Question 162

Question: The value of $ {}^{50}C_4+\sum\limits _{r=1}^{6}{^{56-r}C_3} $ is [AIEEE 2005]

Options:

A) $ ^{56}C_3 $

B) $ ^{56}C_4 $

C) $ ^{55}C_4 $

D) $ ^{55}C_3 $

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ {{}^{50}}C_4+( ^{50}C_3{{+}^{51}}C_3+{{}^{52}}C_3+……{{}^{55}}C_3 ) $ . Taking first two terms together and adding them and following the same pattern, we get $ {{}^{56}}C_4 $ , $ [As{{}^{n}}C _{r}+{{}^{n}}{C _{r-1}}={{}^{n+1}}C _{r}] $ .

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