Discrete Maths - Combinatorics

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11. A box contains 12 socks of white color and 12 socks of black color, all unmatched. A man takes socks out at random in dark. How many minimum socks must he take out to be sure that he has at least two socks of the same color?

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Option : A
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12. Let P(n) be a statement, where n ∈ N, natural numbers. P(1) is true and P(k) ⇒ P(k + 1), for some natural number k. Then P(n) is true for all n.

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Option : B
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13. What is the least value of k such that there must be a pair of numbers from {1, 2, 3, ..., k}, with a sum equal to 9?

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Option : A
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14. Let P(n) : n³ − n is divisible by 4, for all n ∈ N . P (n) is false, because

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Option : B
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15. How many times must we roll a die in order to get the same score?

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Option : D
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