The sum of series `^(20)C_0-^(20)C1+^(20)C2-^(20)C3++^(20)C 10` is

The value of "^20 C_0+^(20)C_1+^(20)C_2+^(20)C_3+^(20)C_4+^(20)C_ 12+^(20)C_ 13+^(20)C_14+^(20)C_15 is a. 2^(19)-(( "^(20)C_10 + "^(20)C_9))/2 b. 2^(19)-((^(20)C 10+2xx^(20)C9))/2 c. 2^(19)-(^(20)C 10)/2 d. none of these

Find the value of ^20 C_0-(^(20)C_1)/2+(^(20)C_2)/3-(^(20)C_3)/4+dot

The value of r for which .^(20)C_(r ), .^(20)C_(r - 1) .^(20)C_(1) + .^(20)C_(2) + …… + .^(20)C_(0) .^(20)C_(r ) is maximum, is

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 sum of the series ^15 C_0+^(15)C_1+^(15)C_2++^(15)C_7dot

The sum 2 xx .^(40)C_(2) + 6 xx .^(40)C_(3) + 12 xx .^(40)C_(4) + 20 xx .^(40)C_(5) + "…." + 1560 xx .^(40)C_(40) is divisible by

Find the sum of the series .^(84)C_(4)+6xx.^(84)C_(5)+15xx.^(84)C_(6)+20xx.^(84)C_(7)+15xx.^(84)C_(8)+6xx.^(84)C_(9)+.^(84)C_(10) .

If a= .^(20)C_(0) + .^(20)C_(3) + .^(20)C_(6) + .^(20)C_(9) + "…..", b = .^(20)C_(1) + .^(20)C_(4) + .^(20)C_(7) + "……"' and c = .^(20)C_(2) + .^(20)C_(5) + .^(20)C_(8) + "…..", then Value of a^(3) + b^(3) + c^(3) - 3abc is

If a= .^(20)C_(0) + .^(20)C_(3) + .^(20)C_(6) + .^(20)C_(9) + "…..", b = .^(20)C_(1) + .^(20)C_(4) + .^(20)C_(7) + "……"' and c = .^(20)C_(2) + .^(20)C_(5) + .^(20)C_(8) + "…..", then Value of (a-b)^(2) + (b-c)^(2) + (c-a)^(2) is

A person predicts the outcome of 20 cricket matches of his home team. Each match can result in either a win, loss, or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct is equal to a. ^20 C_(10)xx2^(10) b. ^20 C_(10)xx3^(20) c. ^20 C_(10)xx3^(10) d. ^20 C_(10)xx2^(20)