find the Coefficient of term x^{2}y^{3} in below expansion:
expansion : (2+x-y+3z)^{10 }^{please write a good description for solution* or how to solve it? * for a person who is a dummy in math and combinatorics...}
80,640. Use the multinomial theorem which says (Basically sum over all non negative integer partitions of n.)
the
basically, it says the powers on the exponents of each term you have in your parenthesis, namely 2,x,y,z must add up to 10.
so how you can write 10 = 0+0+3+7 which is equivalent to
so since you asked for this means since we don't see z so the power of z is 0. 2+3+0+x = 10 and so x = 5 (which is the power 2 is raised to)
so you have = 80640