Question

I would like to know how many combinations of 4 there are in numbers 1 to 15?

Answer 1

Task. How many combinations of 4 there are in numbers 1 to 15?

Solution. Let $(a,b,c,d)$ be any combinations of distinct numbers from $\{1,2,\ldots,15\}$.

Notice that the first number $a$ can be choosen from 15 numbers. Furhter, for every choice of $a$ there remains 14 choices of $b$. Similarly, for any choice of $a,b$ there remains 13 choices of $c$, and finally for any choice of $a,b,c$ there remains 12 choices of $d$. Hence the number of combinations of 4 from $\{1,2,\ldots,15\}$ is equal to

$15*14*13*12=32760.$