Question

Leave your answers as P(n, k), C(n, k)

How many solutions are there to the following equation, if a, b, c, d, e are all
non-negative integers?
a + b + c + d + e = 37

How many solutions are there to the previous equation, if a ≥ 4, and 2 ≤ d ≤ 4 ?

Answer 1

Answer:-

Given that:-

Leave your answers as P(n, k), C(n, k)

How many solutions are there to the following equation, if a, b, c, d, e are all
non-negative integers?
a + b + c + d + e = 37

How many solutions are there to the previous equation, if a ≥ 4, and 2 ≤ d ≤ 4 ?

a+b+c+d+e=37

number of solutions of

are

So, Here

Now, and

for   take

So    

So number of non- negative integer solutions

  

For

  

So

for

So

number of solutions with , and