Permutations And Combinations Question 85

Question: $ ^{47}C_4+\underset{r=1}{\overset{5}{\mathop{\sum }}}{}^{52-r}C_3= $ [IIT 1980; RPET 2002; UPSEAT 2000]

Options:

A) $ ^{6}C_{47} $

B) $ ^{52}C_5 $

C) $ ^{15}C $

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ ^{47}C_4+\sum\limits _{r=1}^{5}{^{52-r}C_3}{{=}^{51}}C_3{{+}^{50}}C_3{{+}^{49}}C_3{{+}^{48}}C_3{{+}^{47}}C_3{{+}^{47}}C_4 $ $ {{=}^{51}}C_3{{+}^{50}}C_3{{+}^{49}}C_3{{+}^{48}}C_3{{+}^{48}}C_4 $ $ {{=}^{51}}C_3{{+}^{50}}C_3{{+}^{49}}C_3{{+}^{49}}C_4 $ $ x_1+x_2+…..+x_6 $ .

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