Answer in Combinatorics | Number Theory for chantelle #30789

Question #30789

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

Expert's answer

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

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

Comments

Natasha Mohanty

19.05.13, 16:56

Here we have 15 numbers and hence n=15 We are taking 4 numbers at a time and that gives us r=4 nCr = n!/(n-r)! r! That gives us, 15!/(15-4)! 4! So, the answer is 1365.