Question

In a parking lot one hundred, one-year-old cars, are parked. Out of them five are to be chosen at random for to check its pollution devices. How many different set of five cars can be chosen?

Answer 1

Number of cars in the parking lot = 100

Number of cars to be selected to check pollution device = 5

Number of ways of selecting 5 cars out of 100 cars

= ¹⁰⁰C₅

= `(100!)/(5! xx (100 - 5)!)`

= `(100!)/(5! xx 95!)`

= `(100 xx 99 xx 98 xx 97 xx 96 xx 95!)/(5! xx 95!)`

= `(100 xx 99 xx 98 xx 97 xx 96)/(5!)`

= `(100 xx 9 xx 98 xx 97 x 96)/(5 xx 4 xx 3 x 2 xx 1)`

= 5 × 33 × 49 × 97 × 96

= 75287520