Question

Dave collects model trains. So far he has 23 distinct train cars. How many ways can he put 7 cars together? = Answer 23 PAnswer 7 =23!(23−7)! =23!16! = Answer 23 ⋅ Answer 22 ⋅21⋅20⋅19⋅18⋅ Answer 17 = Answer

Answer 1

Answer:

He can put 7 cars together in 245,157 ways.

Step-by-step explanation:

The order in which the cars are put together is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

23 distinct train cars. How many ways can he put 7 cars together?

Combinations of 7 from a set of 23. So

$C_{23,7} = \frac{23!}{7!(23-7)!} = \frac{23!}{7!16!} = 245157$

He can put 7 cars together in 245,157 ways.