Consider the expansion of `(a+b+c+d)^(6)`. Then the sum of all the coefficients of the term
Which contains all of `a,b,c,` and d is

Options

A. 2884
B. 4032
C. 1974
D. 2702

Answer

D

Explanation

Sum of coefficient which contains both a and b.
= Number of ways of distributing six distinct objects in four boxes (a,b,c,d)
- Number of ways of distributing six distinct objects in the three boxes (a,c,d)
- Number of ways of distributing six distinct objects in three boxes `(b,c,d)`
+ Number of ways of distributing six distinct objects in two boxes (c,d)
`= 4^(6) - 2 xx3^(6) + .^(2)C_(20 xx 2^(6) = 2702`