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WAEC 2016 · Paper 2 · Q13

  1. (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?

    Separate values with commas, e.g. 3, −2

  2. (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.

Worked solution (try it first)

(a)(i)

  1. Glue each subject into a block.
  2. The 3 blocks can be ordered in 3!=63! = 6 ways.
  3. Inside the blocks: 2!=22! = 2, 5!=1205! = 120 and 3!=63! = 6.
  4. So 6×2×120×6=86406 \times 2 \times 120 \times 6 = 8640.

(ii)

  1. Glue only the 5 Physics books: 1 block and 5 other books make 6 units, 6!=7206! = 720 orders.
  2. Inside the block, 5!=1205! = 120.
  3. So 720×120=86 400720 \times 120 = 86\,400.

(b)

  1. p=1320=0.65p = \frac{13}{20} = 0.65, n=8n = 8.
  2. At least 3 is 1−[P(0)+P(1)+P(2)]1 - [P(0) + P(1) + P(2)].
  3. P(0)=0.358=0.000225P(0) = 0.35^8 = 0.000225, P(1)=8(0.65)(0.35)7=0.003346P(1) = 8(0.65)(0.35)^7 = 0.003346 and P(2)=28(0.65)2(0.35)6=0.021747P(2) = 28(0.65)^2(0.35)^6 = 0.021747.
  4. So 1−0.025318=0.97471 - 0.025318 = 0.9747, which is 0.9750.975 to three significant figures.

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