Question

Counting problem

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{Find the number of natural number solutions of.}\hspace{.33em}\\~\\
& a+2b+c=100 \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

hmm okay

Answer 3

b can be all even numbers

Answer 4

do you know how to solve the simpler version of this problem
a+b+c=100

Answer 5

do i need to change 2b to d

Answer 6

sry i mean 2b is all even numbers

Answer 7

99C2

Answer 8

yeah thats right

Answer 9

i meant to use substitution as 2b=d

Answer 10

here is another way u can think about it
a+b+b+c = 100
how would you solve this
a+b+c+d=100

Answer 11

99C3

Answer 12

i think you would solve
a+b+c=100
and divide by 2

Answer 13

as all the odd possibilities would not possible

Answer 14

u mean 99C2/2

Answer 15

yeah but let me think that might not technically be true
we dont know if odd and even solutions that add to 100 is exactly equal or not

Answer 16

How about calculatinb a+b1+b2+d=100 and substracting something

Answer 17

?

Answer 18

what do u mean

Answer 19

ok back

Answer 20

okay well maybe we can go back to the stars and bars method after this but i think we can do it with just sums

Answer 21

no wait there are 101 WAYs actually to add upto 100
when u pick 2b=0