Evaluate `.^10C_4+^10C_5`

Evaluate: "^10C_5

Evaluate : ""^(13)C_(10)

Evaluate: .^(20)C_(5)+^(20)C_(4)+^(21)C_(4)+^(22)C_(4)

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

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)) .

The number of points of intersection of diagonals which lie within the decagon: ^10 C_2 b. ^10 C_4^ c. ^10 C_6+1 d. 10+^(10)C_2

The value of |(.^(10)C_(4).^(10)C_(5).^(11)C_(m)),(.^(11)C_(6).^(11)C_(7).^(12)C_(m+2)),(.^(12)C_(8).^(12)C_(9).^(13)C_(m+4))| is equal to zero when m is

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

In the expansion off (1+x)^(10)=.^(10)C_(0)+.^(10)C_(1)x+.^(10)C_(2)x^(2)+ . . .+.^(10)C_(10)x^(10) , then value of 528[(.^(10)C_(0))/(2)-(.^(10)C_(1))/(3)+(.^(10)C_(2))/(4)-(.^(10)C_(3))/(5)+ . . .+(.^(10)C_(10))/(12)] is equal to________.

If .^(n)C_(10) = .^(n)C_(15) , then evaluate .^(27)C_(n) .