question_answer

The value of \[^{50}{{C}_{4}}+\sum\limits_{r=1}^{6}{^{56-r}{{C}_{3}}}\]is     AIEEE  Solved  Paper-2005

A) \[^{56}{{C}_{4}}\]          

B)        \[^{56}{{C}_{3}}\]                           

C)        \[^{55}{{C}_{3}}\]               

D)        \[^{55}{{C}_{4}}\]

Correct Answer: A

Solution :

Now,                                                                 \[{{=}^{54}}{{C}_{4}}\,{{+}^{54}}{{C}_{3}}\,{{+}^{55}}{{C}_{3}}\]