Theory question 113
Permutations and Combinations(a) Two different Mathematics books, 5 different Physics books and 3 different Chemistry books are to be arranged on a shelf. How many arrangements are possible if: (i) books on the same subject must stand together? (ii) only the physics books must stand together?
(b) In a certain community, 13 out of every 20 persons speak English. If 8 persons are selected at random from the community, find, correct to three significant figures, the probability that at least 3 of them speak English.
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(a)(i) 3! (order of subjects) × 2! × 5! × 3! = 6 × 2 × 120 × 6 = 8640.
(ii) Treat the 5 Physics books as one block: 6! × 5! = 86 400.
(b) p = 0.65, n = 8: P(X ≥ 3) = 1 − [P(0) + P(1) + P(2)] ≈ 1 − 0.0253 = 0.975.
Glue books that must stay together into one block, then arrange inside it.