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WAEC 2018 · Paper 2 · Q5

A basket contains 4 ripe oranges, 3 unripe oranges and 5 bananas. In how many ways can:

  1. (a)

    1 orange and 1 banana be selected from the basket?

  2. (b)

    3 oranges and 4 bananas be selected from the basket?

  3. (c)

    2 unripe oranges, 1 ripe orange and 3 bananas be selected from the basket?

Worked solution (try it first)
  1. There are 4+3=74 + 3 = 7 oranges and 5 bananas.

(a)

  1.  7C1×5C1=7×5\,{}^7C_1 \times {}^5C_1 = 7 \times 5
    =35= 35 ways.

(b)

  1.  7C3×5C4=35×5\,{}^7C_3 \times {}^5C_4 = 35 \times 5
    =175= 175 ways.

(c)

  1.  3C2×4C1×5C3=3×4×10\,{}^3C_2 \times {}^4C_1 \times {}^5C_3 = 3 \times 4 \times 10
    =120= 120 ways.

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