Question

How many products can be formed from the numbers 2, 3, 4, 5, 6, 7 by taking two or more numbers at a
time?

Answer 1

$n=\{2,3,4,5,6,7\}$

$k_1=2;\;k_2=3.$

Amount of products of the numbers is given by

$$C_n^{k_1}+C_n^{k_2}=\frac{n!}{k_1!(n-k_1)!}+\frac{n!}{k_2!(n-k_2)!}$$ $$=\frac{6!}{2!4!}+\frac{6!}{3!3!}=35.$$