Multiple choice

In how many ways can 3 red berries and 3 blue berries be arranged in a row so that the colours are alternate to each other? (It is to be noted that the berries can be distinguished from each other.)

  1. 60

  2. 62

  3. 68

  4. 72

  5. NA
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D Correct answer
Explanation

Arranging 3 red and 3 blue berries in a row alternately: RBRBRB or BRBRBR. Since berries are distinguishable, there are 3! ways to arrange red and 3! ways to arrange blue. Total = 2 * (3! * 3!) = 2 * 6 * 6 = 72.

AI explanation

The three red berries and three blue berries must be placed in alternating positions, giving exactly two possible color patterns: red-blue-red-blue-red-blue or blue-red-blue-blue-red-blue. For the pattern starting with red, the three red berries can be arranged in 3 factorial ways and the three blue berries can be arranged in 3 factorial ways, giving 6 multiplied by 6 arrangements. Multiplying this by the 2 possible starting colors yields 2 * 6 * 6, which equals 72.

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