Question

The sum of all the coefficient of those terms in the expansion of ${(a+b+c+d)}^8$ which contains $b$ but not $c$ is

• A. $6305$
• B. $4^8-3^8$
• C. Number of ways of forming $8$ digit numbers using digits $1,2,3$ each number as atleast one $3$
• D. Number of ways of forming $4$ digit numbers using digits $1,2,3$ each number as atleast one $3$

Answer 1

Answer: (A)

$6305$

for Sum of coefficients which does not contains $c\left(S_1\right)$,put $a=1,b=1,c=0,d=1$ in $(a+b+c+d{)}^8$

$⟹S_1=(3{)}^8$

for Sum of coefficients which does not contains $c$ and $b\left(S_2\right)$,put $a=1,b=0,c=0,d=1$ in $(a+b+c+d{)}^8$

$⟹S_2=(2{)}^8$

Sum of coefficients which contains $b$ but not $c$ is $3^8-2^8=6305$