Find the coefficient of `a^5b^7in(a-2b)^(12)`

Find the coefficient of a^(5)b^(7) in (a-2b)^(12)

Find the coefficients of x^(7) in (ax^(2)+(1)/(bx))^(11) and x^(-7)in(ax-(1)/(bx^(2)))^(11) and find the relation between a and b so that coefficients are equal.

The coefficient of a^7b^8 in (a+2b+4ab)^(10)=k.2^(18) . Find k.

If the coefficient of x^7 in (x^2+1/(bx))^11 is equal to coefficient at x^-7 in (x+1/(bx^2))^11 Then find value of b

Find the coefficient of x^(7) in the expansion of (ax^(2) + (1)/(bx))^(11) . (ii) the coefficient of x^(-7) in the expansion of (ax + (1)/(bx^2))^(11) . Also , find the relation between a and b , so that these coefficients are equal .

Find the coefficient of (i) x^(5)" in the expansion of "(x+3)^(8) (ii) x^(6) " in the expansion of "(3x^(2) - a/(3x))^(9) (iii) x^(-15) " in the expansion of " (3x^(2) - a/(3x^(3)))^(10). (iv) a^(7)b^(5)" in the expansion of "(a-2b)^(12) .

If the sum of the coefficients in the expansion of (1-4x+7x^(2))^(n) is "a" and the sum of the coefficients of (1+x+2x^(2))^(n) is "b" ,then find relation between a and b

What are binomial coefficients in (a+b)^(7) ?