Question

How many ways can four numbers be drawn from a group of ten numbers if the order does not matter?

Answer 1

Answer:

210 ways

Step-by-step explanation:

Simply put in combinations and permutations,

ORDER MATTERS >> PERMUTATION

ORDER DOESNT MATTER >> COMBINATION

Formula for Permutation is  $P(n,r)=\frac{n!}{(n-r)!}$

Formula for Combination is  $C(n,r)=\frac{n!}{(n-r)!r!}$

These means taking r objects from a group of n

Also x! means x(x-1)(x-2)... (ex: 4! = 4 * 3 * 2 * 1)

Now, from the question, we have "order doesn't matter" so we have combination with n = 10 and r = 4.

Let's put the numbers into formula and find the answer:

$C(n,r)=\frac{n!}{(n-r)!r!}\\C(10,4)=\frac{10!}{(10-4)!4!}\\=\frac{10!}{6!4!}\\=\frac{10*9*8*7*6!}{6!4!}\\=\frac{10*9*8*7}{4*3*2*1}\\=210$

So, the answer is 210