Let x be the number of biscuits the person select from first variety, y from the second, z from the third and w from the fourth variety. Then the number of ways = number of solutions of the equation
x + y + z + w = 10.
where x = 1, 2, .........,7
y = 1, 2, .........,7
z = 1, 2, .........,7
w = 1, 2, .........,7
This is equal to = coefficient of x10 in (x + x2 + ...... + x7)4
= coefficient of x6 in (1 + x + ....... + x6)4
= coefficient of x6 in (1 – x7) 4 (1 – x)–4
= coefficient x6 in (1 – x)–4
