How many integer solutions are there to the equation x1 x2

How many integer solutions are there to the equation x_1 + x_2 + x_3 + 2x_4 + x_5 = 72 where x_1 greaterthanorequalto 2, x_2, x_3 greaterthanorequalto 1, and x_4, x_5 greaterthanorequalto 0.

Solution

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Kindly note that in order toalculate the number of integer solutions to the given question, there is a direct formulae available

Step 1: Sample space = 72-2-1-1 = 68 (Subtracting the minimum values of 5 variables)

Step 2:- Total Number of variables = 5

Solution is ^68+5-1C_5-1

= ⁷²C₄

=1028790 Integers