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Statistics - Permutations and combinations

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11. If a five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition, then total number of ways this can be done is

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12. If sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them, then total number of triangles that can be constructed by using these points as vertices, is

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13. A student can take one of four Mathematics sections and one of five English sections. The number n of ways he can register for the two courses, is

  • Option : C
  • Explanation : There are four choices for Mathematics and five choices for English. n= 4 x 5= 20
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14. There are 10 lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated is

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15. The number of ways in which 10 persons can sit around a circular table so that none of them has the same neighbours in any two arrangements, is

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Permutations and combinations