The coefficient of x7 in 1+3x−2x310is equal to

The coefficient of x7 in 1+3x−2x310=∑10!n1!n2!n3!(1)n1(3)n2(−2)n3where n1+n2+n3=10,n2+3n3=7Different possibilities are as follown1n2n3370541712∴ Coefficient of x7=10!3!7!(1)3(3)7(−2)0+10!5!4!1!(1)5(3)4(−2)1+10!7!1!2!(1)7(3)1(−2)2=62640