Cards are down at random from a pack of 200 cards numbered

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Cards are down at random from a pack of 200 cards numbered 1 to 200. Find the probability of drawing a number which is a perfect cube ?

1. 1/40
2. 3/40
3. 7/40
4. 19/40

Correct Option: A

Total number of ways of selecting 1 card from 200 cards is ²⁰⁰C₁ ways.
Let E be an event of drawing a number which is a perfect cube.
E = {1, 8, 27, 64, 125 }
∴ P(E) = n(E) / n(S)
= ⁵C₁ / ²⁰⁰C₁ = 5/200 = 1/40