Question

Find the value of 10C0 +10C1 + 10C2+.......+10C10

Answer 1

$^{10}C_0+^{10}C_1+^{10}C_2+.......+^{10}C_{10}$ = 2048

Step-by-step explanation:

We have,

$^{10}C_0+^{10}C_1+^{10}C_2+.......+^{10}C_{10}$

To find, the value of $^{10}C_0+^{10}C_1+^{10}C_2+.......+^{10}C_{10}=?$

∴$^{10}C_0+^{10}C_1+^{10}C_2+.......+^{10}C_{10}$

           1  This can be called the zero row, and Sum $=$ 1

    1                1 This can be called the first row, and Sum $=2^{1}=2$

   1           2               1 This can be called the third row, and Sum $=2^{2}=4$

 1        3           3               1 This can be called the third row, and Sum $=2^{3}=8$

∴$^{10}C_0+^{10}C_1+^{10}C_2+.......+^{10}C_{10}$

$=2^{11}=2048$

Hence, $^{10}C_0+^{10}C_1+^{10}C_2+.......+^{10}C_{10}$ = 2048