Questions on Permutation and Combination

What is Permutation?

A Permutation is the arrangement of “n-distinct” objects taken “r” at a time without regard given to the other of the arrangement.

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A Combination is the selection of “n-different” objects taken “r” at a time with attention given to the order of arrangement. (kindly use the comment box below to ask a question).

Questions on Permutation and Combination

  1. Evaluate the following
  • 5P4
  • 6P3
  • 10P7


  1. Evaluate these
  • 5C4
  • 6C3
  • 10C7


  1. In how many ways can twelve mathematics textbooks be arranged in a bookshelf taking two at a time?


  1. Five people attended a send-off party. If there are five seats, in how many ways could they be seated if they sit anyhow?
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  1. In how many ways five identical physics textbooks, four chemistry textbooks, and two biology textbooks can be arranged?


  1. A committee comprises of three male and two female students are to be formed out of eight male and female students available. How many such committees could be formed.


  1. The Rector, her female secretary and five senior principal officers of the college were invited to a meeting. In how many ways can they be seated if;
  • They can sit anyhow?
  • The rector must seat next to her secretary?


  1. If there are ten men, seven women, six boys, and six girls. A committee consisting of five men, three women, two boys, and two girls is to be constituted. How many such committees could be formed if;
  • There is no restriction?
  • One man and one woman must be included?
  • One man and one girl must be excluded?
  • One woman and two boys must be included?
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  1. In how many ways can ten different books be arranged on a bookshelf taking three at a time?


  1. A family has seven males and three female children. In how many ways can five males and two female children be selected to represent the family?

Other Mathematics Questions

  1. Co-ordinate Geometry
  2. Linear Programming
  3. Set Theory
  4. Empirical Probability
  5. Integration & Vector Algebra
  6. Differentiation

Video on Permutation and Combination