You have ten cars how many options is that

Question

A boy has 10 different cars. He may take 1,2,3,4,5,6,7,8,9,10 or no cars. How many options does the boy have for taking matchbox cars on vacation?

Answer 1

No cars or all cars: 1 way

1 or 9 cars: 10 ways

2 or 8 cars: 10*9/2=45 ways

3 or 7 cars: 10*9*8/(3*2)=120 ways

4 or 6 cars: 10*9*8*7/(4*3*2)=210 ways

5 cars: 10*9*8*7*6/(5*4*3*2)=252 ways

TOTAL: 1024 ways (sum of coefficients for 10th row of Pascal’s Triangle or binomial expansion of (1+x)¹⁰).