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प्रश्न
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?
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उत्तर
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
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