Question

The coefficient of $t^4$ in $(1-t{)}^6{\left(1+t^2\right)}^5$ is equal to

Answer 1

Answer: 100

The coefficient of $t^4$ in $(1-t{)}^6{\left(1+t^2\right)}^5$
$={}^6{C}_0{}^5{C}_2+{}^6{C}_2\cdot {}^5{C}_1+{}^6{C}_4\cdot {}^5{C}_0$
$=(1)(10)+(15)(5)+(15)(1)$
$=10+75+15=100$