Professor Halfbrain has 10 books on mathematics, 8 books on chemistry and 5 books on astrology (he’s a Gemini). He is packing for vacation, and hastily throws 7 books into his suitcase. What is the probability that he has selected at least 2 books from each subject?

0.09

Step-by-step explanation:

All the possible outcomes are listed below if the condition of at least 2 books from each subject has to be satisfied

Option 1 - 3 books from mathematics, 2 books from chemistry and 2 books from astrology

Option 2 - 2 books from mathematics, 3 books from chemistry and 2 books from astrology

Option 3 - 2 books from mathematics, 2 books from chemistry and 3 books from astrology

The probability for option 1 = 3/10 x 2/8 x 2/5

= 0.03

The probability for option 2 = 2/10 x 3/8 x 2/5

= 0.03

The probability for option 3 = 2/10 x 2/8 x 3/5

= 0.03

The final probability = Probability of option 1 +  Probability of option 2 + Probability of option 3

= 0.09

Note: The order does not matter because it is given that he is packing for vacation, and HASTILY throws 7 books into his suitcase.

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.

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