AP ICET 2015

Question 124

If $$C_r = ^{10}C_r$$, for $$0 \leq r \leq 10$$, then $$2C_0 + 3C_1 + 4C_2 + ......... + 11C_{10} =$$

Solution

Solution

$$2.^{10}C_0$$ +$$3.^{10}C_1$$ + $$4.^{10}C_2$$.....

=$$2.1\ +\ \frac{3.10!}{1!9!}\ +\frac{4.10!}{2!8!}\ +\frac{5.10!}{3!7!}$$

=  2 + 30 + 180 + 600...


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