Find the sum
`2..^(10)C_(0) + (2^(2))/(2).^(10)C_(1) + (2^(3))/(3).^(10)C_(2)+(2^(4))/(4).^(10)C_(3)+"...."+(2^(11))/(11).^(10)C_(10)`.

Find the values of .^(10)C_(4)

Find the value of .^10 C_2

Find the value of (.^(10)C_(10))+(.^(10)C_(0)+.^(10)C_(1))+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2))+"...."+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2)+"....." + .^(10)C_(9)) .

Find the value of .^11 C_10

The value of (.^(21)C_(1) - .^(10)C_(1)) + (.^(21)C_(2) - .^(10)C_(2)) + (.^(21)C_(3) - .^(10)C_(3)) + (.^(21)C_(4) - .^(10)C_(4)) + … + (.^(21)C_(10) - .^(10)C_(10)) is

Find the sum .^(10)C_1+^(10)C_3+^(10)C_5+^(10)C_7+^(10)C_9

Find the value of .^(20)C_(0) xx .^(13)C_(10) - .^(20)C_(1) xx .^(12)C_(9) + .^(20)C_(2) xx .^(11)C_(8) - "……" + .^(20)C_(10) .

Find the value of .^(20)C_(0) - .^(20)C_(1)+ .^(20)C_(2) - .^(20)C_(3) +"……"-"....." + .^(20)C_(10) . is

Given are six 0' s, five 1' s and four 2's . Consider all possible permutations of all these numbers. [A permutations can have its leading digit 0 ]. How many permutations have the first 0 preceding the first 1 ? (a) "^(15)C_(4)xx^(10)C_(5) (b) "^(15)C_(5)xx^(10)C_(4) (c) "^(15)C_(6)xx^(10)C_(5) (d) "^(15)C_(5)xx^(10)C_(5)

Find the value of ((1)/(4^(-3))-(2)/(10^(-2)))/((1)/(2^(-2))+(1)/(4^(-1)))