i am studying for a discrete math final and i do not understand the provided solution. specifically, how to rationalize "c(12,10) = c(12,2)". be as specific and detailed as possible.
how many solutions does the equation have, x1 + x2 + x3 = 10, where x1, x2, and x3 are non-negative integers?
to count the number of solutions, we note that a solution corresponds to the ways of selecting 10 items fro m a set with three elements so that x1 items of type one, x2 items of type two, x3 items of type three. hence, the number of solutions is equal to the number of 10 - combinations with repetitions allowed from a set with three elements. from theorem 2, the equation has c(3 + 10−1, 10) = c(12,10) = c(12,2) = 66 solution

Step-by-step explanation:

Given is an equation in three variables

where the three variables are non negative integers.

Since sum =10, and each integer has minimum value 1, we find that each variable can take values as 1,2,...8 only

If first variable is 1, the other two can be 1,8  or 2,7 or... 8,1  ... 8 ways

If first variable is 2, ...   the other two can be 1,7  or 2,6 or..7,1 ... 7 ways

This will go up to first variable =8

Thus we have total number of solutions as

Thus possible solutions are 36                              

answer: sensy

step-by-step explanation:

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph