Question

How many different groups if 35 cars can be formed from 40 cars?

Answer 1

658,008 .........................

Answer 2

Answer:

$C(40,35)=40C_3_5=658008$

Step-by-step explanation:

We can use Combinatorics in order to solve this problem. Combinatorics is the part of Mathematics that studies the various ways of grouping with the elements of a set, forming them and calculating their number. There are different ways of making these groupings. Depending on whether the elements are repeated or not, we can use a permutation or a combination.

A permutation of a set of elements is an arrangement of said elements taking into account the order. A combination of a set of elements is a selection of those elements regardless of order. In this case, the order doesn't matter, hence, this is a combination. The number of k-permutations of n elements is given by:

$C(n,k)=nC_k=\frac{n!}{k!(n-k)!}$

Where:

$n=40\\k=35$

Therefore, the different groups that can be formed are:

$C(40,35)=\frac{40!}{35!(40-35)!} =658008$