Question

Can someone solve these for me?

Consider the equation X1 X2X3 + X4+X5 40. How many different solutions does this equation have if all the variables must be positive integers? Enter the exact numeric answer QUESTION 2 Suppose that a license plate consists of three letters followed by three digits. How many different license plates start with the letter A if letters and digits cannot be repeated? Enter the exact numeric answer.

Answer 1

1) given each should be positive, So, each should be at least 1.

    remaining 35 should be distributed among 5.

    number of ways = (n+r-1) _c(r-1)

                                          = (35+5-1)_c(5-1)

                                          = 82251

2) first letter is fixed i.e. A, remaining 25 alphabets and 2 letters need to be arranged

    no ways = 25 * 24 = 600

    next 3 digits need to be arranged out of 10 digits

    no of ways = 10 * 9 * 8 = 720

    Total no of ways = 600 * 720 = 432000