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  • Can someone explain - Binomial theorem and its simple applications - JEE Main

The value of ^{50}C_{4}+\sum_{r=1}^{6}\: ^{56-r}C_{3}\; is

  • Option 1)

    ^{56}C_{4}\; \;

  • Option 2)

    \; ^{56}C_{3}\;

  • Option 3)

    \; ^{55}C_{3}\; \;

  • Option 4)

    \; ^{55}C_{4}

 

Answers (1)

best_answer

As we have learned

Properties of Binomial Theorem -

\dpi{120} \frac{^{n}c_{r-1}}{^{n}c_{r}}= \frac{r}{n-r+1} and

^{n}c_{r}+^{n}c_{r+1}= ^{n+1}c_{r+1}

-

 

 ^{50 }C_4+(^{55}C_3+^{54}C_3+^{53}C_3+^{52}C_3+^{51}C_3+^{50}C_3)

=^{50 }C_4+(^{50}C_3+^{51}C_3+^{52}C_3+^{53}C_3+^{54}C_3+^{55}C_3)  after rearranging 

=(^{51 }C_4+^{51}C_3+^{52}C_3+^{53}C_3+^{54}C_3+^{55}C_3)

=(^{52 }C_4+^{52}C_3+^{53}C_3+^{54}C_3+^{55}C_3)  (proceeding in similar way )

=(^{56 }C_4

 

 

 

 

 


Option 1)

^{56}C_{4}\; \;

Option 2)

\; ^{56}C_{3}\;

Option 3)

\; ^{55}C_{3}\; \;

Option 4)

\; ^{55}C_{4}

Posted by

gaurav

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